For Question 1-4, We will load 1000_Companies.csv dataset that contains data belongs to 1000 companies such as R&D, administration and marketing spendings and location. We will use this data to build a machine learning based decision suppport system model to predict companies' profit.

Question 1: 10 Points (Load Data)

• (A) Load the "1000_Companies.csv" dataset - 5 points
• (B) Display the first and last 5 rows of this dataset - 5 points

In [ ]:

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Question 2: 15 Points (Manipulate Data)

• (A) Extract the independent (Feature Matrix) and dependent (target vector) variables. - 5 points

• (B) Encode the categorical data following the following steps:

  1) Integer Encoding - 5 points

  2) One-Hot Encoding - 5 points

In [1]:

#(A)Extract the independent (Feature Matrix) and dependent (target vector) variables.

​

​

#(B)Encode the categorical data following the following steps

##1)Integer Encoding

​

##2) One-Hot Encoding

​

Question 3: 35 Points (Modeling)

• (A) Split the dataset into the training and test sets. Hint: Use train_test_split(test_size=0.3, shuffle = False) - 5 points
• (B) Use Linear Regression Modeling to train your model (Name your model as Model1_LRM) - 5 points
• (C) Use the trained model (Model1_LRM) and the test dataset for prediction - 5 points
• (D) Calculate the accuracy of your Model1_LRM model. Hint: Use r2_score from sklearn.metrics - 5 points
• (E) Use Random Forest Regressor Modeling to train your model (Name your model Model2_RFR) - 5 points
• (F) Use the trained model(Model2_RFR) and the test dataset for prediction - 5 points
• (G) Calculate the accuracy of your Model2_RFR model. Hint: Use r2_score from sklearn.metrics - 5 points

In [2]:

#(A) Split the dataset into the training and test sets. Hint: Use train_test_split(test_size=0.3, shuffle = False)

​

#(B) Use Linear Regression Modeling to train your model (Name your model as Model1_LRM)

​

#(C) Use the trained model (Model1_LRM) and the test dataset for prediction

​

#(D) Calculate the accuracy of your Model1_LRM model. Hint: Use r2_score from sklearn.metrics

​

In [28]:

#(E) Use Random Forest Regressor Modeling to train your model (Name your model Model2_RFR)

​

#(F) Use the trained model(Model2_RFR) and the test dataset for prediction

​

#(G) Calculate the accuracy of your Model2_RFR model. Hint: Use r2_score from sklearn.metrics

​

Out[28]:

0.724613670616963

Suppose the Super Bowl is this week, and Carlos is in need of a television to watch the big game. As a college student, Carlos knows that he can either buy his flat-screen television at the local electronics store, or he can shop online for a better deal but have to wait four days for the television to arrive. The following problem uses the economic concept of rate of time preference to help determine which decision is better for Carlos. Throughout the question, assume that Carlos pays for the good the day he buys it, so his wealth is affected in the initial time period no matter where he buys the good. Also, assume the shipping cost and cost to travel to the store are incorporated into their respective given prices. Finally, assume the goods are identical, and there’s no cost to gaining information about prices—in other words, he knows the best price online and in the store without having to search.

Suppose Carlos receives a utility of 45.36 utils once he actually receives his television. Let β indicate Carlos’s patience level; that is, β represents the discount rate between consuming something today versus tomorrow.

For each value of β in the following table, compute the present value of Carlos’s utility from receiving the television when he purchases his television in the store (and receives it today) and when he purchases it online (and receives it four days from now).

present value when...

Where Purchased      β=0.9 β=0.6 β=0.3

Store (received today) --------- ---------- ----------

Online (received in four days) ---------- ---------- ----------

If Carlos buys his television in the store, it costs $500; whereas if he buys it online, it costs only $310. Suppose the utility Carlos receives as a function of his wealth can be expressed in the following way: U(W)=W0.7 . If Carlos’s level of wealth is $1,300 before purchasing a television, his utility from wealth will be ---------- utils if he purchases his television in the store, or ----------- utils if he purchases it online.

Assume Carlos’s total utility from purchasing a television is the sum of the present value of his utility from consumption and the utility from his remaining wealth.

For each level of β , complete the following table with Carlos’s total utility.

Total utility when...

Where Purchased   β=0.9 β=0.6 β=0.3

Store ----------- ---------- ----------

Online ------------ ----------- -----------

From the previous analysis, you can conclude that as β increases, consumers become ---------- patient. This indicates that as β approaches one, consumers are more likely to purchase the good -----------

Which statement is true?

Select one:

a. To have economic growth, we must have zero unemployment.

b. On the production possibilities frontier, unemployment is zero percent.

c. To get out of a recession, we must move to some point closer to the production possibilities frontier.

d. On the production possibilities frontier, 85 percent of the labor force is employed.

Which of the following is true?

Select one:

a. Keynes suggested that savers save and investors invest for different reasons.

b. According to Keynes, an equilibrium below full employment was a rare occurrence.

c. To fight a depression, Keynes said that the government should spend money on carefully chosen projects.

d. Keynes believed the economy was basically stable.

Which is the most accurate statement?

Select one:

a. Our trade problems with Japan and China are very similar.

b. Our trade deficits with Japan and China account for almost our entire trade deficit.

c. If Japan and China traded fairly, our trade deficits with those two countries would disappear.

d. Japanese markets have been at least somewhat closed to imports.

Which statement is true?

Select one:

a. X_n had been positive from 1900 until the 1970s.

b. X_n has always been negative.

c. X_n has always been positive.

d. X_n had been negative from 1900 until the 1970s.

Which of the following statements is FALSE?

Select one:

a. Until the early 1980s Americans were investing much more in foreign countries than foreigners were in the U.S.

b. Our capital and current accounts add up to zero.

c. None of these is false.

d. Foreigners have reinvested most of the dollars they have earned trading with us in U.S. government and corporate securities, real estate, and direct investment in plant and equipment.

Which of the following statements is true?

Select one:

a. Virtually all of the poor receive food stamps, but not public assistance.

b. Virtually all of the poor receive public assistance and food stamps.

c. None of these is true.

d. Virtually all of the poor receive public assistance, but not food stamps.

Which of the following is true?

Select one:

a. Southern manufacturers benefited from high protective tariffs of the 19th century that kept out cheaper Japanese manufactured goods.

b. The completion of the transcontinental railroad system in the 1880s eventually made the U.S. the world's first mass market.

c. Agricultural inventions such as John Deere's steel plows did little to improve farm productivity.

d. The canal system linking east-coast rivers with the Great Lakes in the 1820s created an "American economy" rather than just a series of regional economies located in one country.

Which of the following statements is true?

Select one:

a. Every nation should try to be completely self-sufficient.

b. The basis for international trade is specialization.

c. International trade lowers our standard of living.

d. Importing consumer products increases our prices.

Which statement is true?

Select one:

a. Most taxpayers pay more in payroll tax than in personal income tax.

b. A person earning $100,000 pays $10,000 in payroll tax.

c. The Medicare tax rate is 6.2 percent.

d. There is no such thing as a regressive tax.

Which statement is true?

Select one:

a. To have economic growth, we must have zero unemployment.

b. On the production possibilities frontier, unemployment is zero percent.

c. To get out of a recession, we must move to some point closer to the production possibilities frontier.

d. On the production possibilities frontier, 85 percent of the labor force is employed.

I would like to get the step by step solution for the below question

Question 11 pts

What is the difference between positive economics and normative economics?

Group of answer choices

Positive economics deals with dynamic systems, while normative economics focuses on static systems.

Normative economics deals with how the world actually works, whereas positive economics focuses on what people ought to do.

Positive economics requires making value judgments, while normative economics relies solely on factual statements.

Normative economics applies in cases that are characterized by typical or normal behaviors and dynamics, while positive economics applies in cases with unusually rapid technological progress.

Normative economics focuses on what people ought to do, whereas positive economics deals with how the world actually works.

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Question 21 pts

Which of the following are true statements about public goods?

Group of answer choices

To find the aggregate marginal willingness to pay (MWTP) for the good you would add together the individual MWTP corresponding to given ``output'' levels

The good is available in the same quantities to everyone

Payment of a fee to a public agency provides access to the good

The total amount consumed is the sum of the amounts consumed by each individual

Public goods are those paid for by taxes and provided and maintained by the government

Overuse by some diminishes the amount available to others

They are rival and non-excludable

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Question 31 pts

Angela is willing to pay $75 now for an item to be delivered in exactly 3 years time. The most she would be willing to pay for the item today is $100. What is Angela's discount rate?

Group of answer choices

7.5% per year

25% per year

15% per year

10% per year

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Question 41 pts

Aubrey consumes 5 units of a certain good. Aubrey would buy one additional unit only if the price per unit were $10 or less. What concept is being illustrated here?

Group of answer choices

Diminishing marginal utility

Marginal willingness to pay

Discounting

Aggregate willingness to pay

Intrinsic value

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Question 51 pts

A local firm makes and sells handcrafted equestrian riding boots. Some of the residual chemicals from the leather tanning process are discharged into a river used for the town's drinking water supply. The social marginal cost curve for the riding boots is ___________________ the firm's riding boot supply curve.

Group of answer choices

lower than

higher than

completely unrelated to

equal to

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Question 61 pts

Last week you paid $20 for a ticket to the opening game of the Cowboy's upcoming football season. Tickets are now sold out, and your acquaintance, Mary, asks to buy your ticket. The lowest price at which you would be willing to sell your ticket to Mary is $50, but she is willing to pay no more than $40. If attending the game and selling your ticket to Mary are your only two options, what is your opportunity cost of going to the game?

Group of answer choices

$50

$20

$40

$30

$0

$10

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Question 71 pts

Which one or more of the following statements is consistent with the economic definition of sustainability for a nonrenewable natural resource?

Group of answer choices

Non-renewable resources cannot be used sustainably because they eventually will run out; only renewable resources can be used sustainably.

Sustainability requires that the rate of extraction must be less than the discount rate in all periods.

Use of a non-renewable resource can be sustainable if investments in other forms of productive capital are made in an amount equal to or exceeding the user cost.

Extraction can be sustainable only if it is matched or exceeded by the rate of discoveries of new deposits.

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Question 81 pts

Which of the following are typically associated with open-access resources?

Group of answer choices

rivalry

over-use relative to the economically efficient level

resource discounting inflation

Under-supply relative to the economically efficient level due to free-riding

Public goods

Private goods

excludability

resource rent dissipation

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Question 91 pts

If the government charges a tax to producers in the amount of $x per unit of output, this has the effect of...

Group of answer choices

Decreasing the market quantity

Shifting the marginal external cost curve down

Shifting the supply curve up

Shifting the marginal external cost curve up

Increasing the market quantity

Decreasing the market price

Shifting the demand curve up

Shifting the supply curve down

Increasing the market price

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Question 101 pts

The table below shows the consumer surplus per visitor that would be generated at different levels of attendance at a local public park that currently charges no fee for entry. Consumer surplus per visitor declines with the number of visitors because of crowding and congestion in the park.

Number of visitors	Consumer surplus per visitor
200	50
300	40
400	20
500	0
600	-10
700	-15
800	-20

What entry fee would need to be charged to limit the number of visitors to the level that maximizes total surplus?

Group of answer choices

$60

$40

$20

$50

$0

$30

$10

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Question 111 pts

A project has been proposed to build an overlook area off the Snowy Range Scenic Byway. To finance the construction of the overlook, a two-tier tax will be assessed on residents of Laramie and several nearby towns. Households below the median income will pay 0.1% of their income in taxes, and those above the median income will pay 0.2%. Differences in households' willingness-to-pay for the overlook have been found to be unrelated to their incomes.

Based on the information provided, which one or more of the following conclusions can we draw about the distribution of the benefits, costs, and net benefits of the proposal relative to household incomes?

Group of answer choices

Net benefits are distributed regressively

Costs are distributed regressively

Benefits are distributed progressively

Net benefits are distributed progressively

Costs are distributed proportionally

Net benefits are distributed proportionally

Benefits are distributed regressively

Benefits are distributed proportionally

Costs are distributed progressively

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Question 121 pts

Which of the following are reasons why voluntary contributions to The Nature Conservancy probably would not correspond to the total value that people place on the wildlife habitat protected by that organization?

Group of answer choices

Travel costs may be prohibitive for some contributors.

Protection of species habitat is a public good.

The protected habitat also may provide consumptive or non-consumptive use values.

The marginal private cost of protecting the habitat will be greater than the marginal social benefits.

Existence values cannot be measured using a contingent valuation approach.

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Question 131 pts

Use the table below to answer the questions that follow.

Time period	Project A benefit	Project A cost	Project B benefit	Project B cost
0	10	25	40	120
1	25	25	40	0
2	40	25	40	0
3	50	25	40	0

Recall that a project's internal rate of return (IRR) is the discount rate for which the project's present value of net benefits equals zero.

(a) The internal rate of return for Project A is                            [ Select ]                       ["equal to", "greater than", "less than"]         0.3 per period.

(b) The internal rate of return for Project B is                            [ Select ]                       ["equal to", "greater than", "less than"]         0.3 per period.

(c) If the discount rate is 0.1 per period and only one project an be adopted, an economist would recommend                            [ Select ]                       ["Project B", "Project A"]         .

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Question 141 pts

In Java

The Problem

In his book Irreligion, the mathematician John Allen Paulos tells an amusing story about the Dutch astronomer Cornelis de Jager, "who concocted the following algorithm for personalized physical constants, [and] used it to advance a charming theory about the metaphysical properties of Dutch bicycles." First select any positive real-valued universal physical or mathematical constant that seems interesting to you, e.g., π, e, Planck's constant, the atomic weight of molybdenum, the boiling point of water in Kelvin, whatever you like. Call this constant μ. Then select any four positive real numbers not equal to 1 that have personal meaning to you, e.g., your favorite number, day or month or year of birth, age in fortnights or seconds, weight in stones or grams, height in furlongs or millimeters, number of children, house number, apartment number, zip code, last four digits of SSN, whatever you like. Call these four personal numbers w, x, y, and z.

Now consider the de Jager formula w^ax^by^cz^d, where each of a, b, c, and d is one of the 17 numbers {-5, -4, -3, -2, -1, -1/2, -1/3, -1/4, 0, 1/4, 1/3, 1/2, 1, 2, 3, 4, 5}. The "charming theory" asserts that the de Jager formula with your four personal numbers can be used to approximate μ within a fraction of 1% relative error. For example, suppose you choose to approximate the mean distance from the earth to the moon in miles: μ = 238,900. And suppose you are an OSU sports fan, so your personal numbers are the number of wins in OSU's last national championship season (14), the seating capacity of Ohio Stadium (102,329), the year of Jesse Owens' four gold medals in Berlin (1936), and your jersey number when you played high school field hockey (13). Then the value of 14^-5102329¹1936^1/213⁴ is about 239,103, which is within about 0.08% of μ.

Your job is to create a Java program that asks the user what constant μ should be approximated, and then asks in turn for each of the four personal numbers w, x, y, and z. The program should then calculate and report the values of the exponents a, b, c, and d that bring the de Jager formula as close as possible to μ, as well as the value of the formula w^ax^by^cz^d and the relative error of the approximation to the nearest hundredth of one percent (see SimpleWriter print(double, int, boolean) for a method you may find useful for this). Note that your program must find the combination of exponents that minimizes the error of the approximation of μ and then print the exponents, best approximation, and corresponding relative error. (Essentially this program could be used to disprove the "charming theory" by finding μ, w, x, y, and z such that the best approximation of μ results in a relative error that is greater than 1%.)

Method

1. Create a new Eclipse project by copying ProjectTemplate or a previous project you have created, naming the new project Pseudoscience. In the src folder of this project and the default package, create a class called ABCDGuesser1.
2. Edit ABCDGuesser1.java to satisfy the problem requirements stated above, as well as the following additional requirements:
   • Use only while loops for iteration.
   • Check that the inputs provided by the user are valid, i.e., the input for μ is a positive real value and the inputs for w, x, y, and z are each a positive real value not equal to 1. You should implement and use two new static methods declared as follows:

     1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23

     /** * Repeatedly asks the user for a positive real number until the user enters * one. Returns the positive real number. * * @param in *            the input stream * @param out *            the output stream * @return a positive real number entered by the user */ private static double getPositiveDouble(SimpleReader in, SimpleWriter out) {...}    /** * Repeatedly asks the user for a positive real number not equal to 1.0 * until the user enters one. Returns the positive real number. * * @param in *            the input stream * @param out *            the output stream * @return a positive real number not equal to 1.0 entered by the user */ private static double getPositiveDoubleNotOne(SimpleReader in, SimpleWriter out) {...}

     Note that you cannot assume the user will provide a number; the user can type pretty much anything. So your methods should read the input as a String (use SimpleReader nextLine() method), then make sure that the input is a real number (use FormatChecker.canParseDouble()), and finally convert the string to a double (use Double.parseDouble()).
3. Copy ABCDGuesser1.java to create ABCDGuesser2.java. Change it so the while loops in the main method are replaced by for loops (but you should not change the loops in the bodies of getPositiveDouble and getPositiveDoubleNotOne), and so it uses at least one additional private static method.

1, An engineer wanted to determine how the weight of a car affects gas mileage. The accompanying data represent the weights of various domestic cars and their gas mileage in the city for a certain model year. Suppose that we add Car 12 to the original data. Car 12 weighs 3,305 pounds and gets 19 miles per gallon. Complete parts​(a) through​ (f) below.

Car	Weight (lbs)	Miles per Gallon
1	3765	19
2	3984	18
3	3590	21
4	3175	22
5	2580	27
6	3730	18
7	2605	26
8	3772	17
9	3310	20
10	2991	25
11	2752	26

(b) Compute the linear correlation coefficient with Car 12 included.

The linear correlation coefficient with Car 12 included is r =

​(Round to three decimal places as​ needed.)

(c) Compare the linear correlation coefficient of the part? (b) with the linear correlation coefficient for the original data. Why are the results here? reasonable?

i) The correlation coefficient changed significantly when Car 12 was added. This is reasonable since Car 12 does not follow the pattern of the original data.

ii) The correlation coefficients both indicate a strong negative correlation. This is reasonable since Car 12 does not follow the pattern of the original data.

iii) The correlation coefficients both indicate a strong negative correlation. This is reasonable since Car 12 roughly follows the pattern of the original data.

d) Now suppose that we add Car 13? (a hybrid? car) to the original data? (remove Car? 12). Car 13 weighs 2,890 pounds and gets 60 miles per gallon. Draw the scatter diagram with Car 13 included.

e) Compute the linear correlation coefficient with Car 13 included.

2, Researchers wondered whether the size of a​ person's brain was related to the​individual's mental capacity. They selected a sample of 5 females and 5 males and measured their MRI counts and IQ scores. The data is reported to the right. Complete parts ​(a) through ​(d) below.

Females_MRI	Females_IQ	Males_MRI	Males_IQ
951545	137	1001121	140
833868	132	1038438	139
856472	140	1079550	141
866662	130	924059	135
857782	133	949589	144

Critical Values for Correlation Coefficient

n
3	0.997
4	0.950
5	0.878
6	0.811
7	0.754
8	0.707
9	0.666
10	0.632
11	0.602
12	0.576
13	0.553
14	0.532
15	0.514
16	0.497
17	0.482
18	0.468
19	0.456
20	0.444
21	0.433
22	0.423
23	0.413
24	0.404
25	0.396
26	0.388
27	0.381
28	0.374
29	0.367
30	0.361

​(a) Draw a scatter diagram treating MRI count as the explanatory variable and IQ as the response variable. Choose the correct diagram below.

(b) Compute the linear correlation coefficient between MRI count and IQ. Are MRI count and IQ linearly​ related? Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice.

​(Round to three decimal places as​ needed.)

A.​Yes, MRI count and IQ are linearly related since the linear correlation coefficient is

B.​No, MRI count and IQ are not linearly related since the linear correlation coefficient is

​(c) Draw a scatter​ diagram, but use a different plotting symbol for each gender. Choose the correct diagram below.

​(d) Compute the linear correlation coefficient between MRI count and IQ for females. Compute the linear correlation coefficient between MRI count and IQ for males.

The linear correlation coefficient for females is

The linear correlation coefficient for males is

​(Round to three decimal places as​ needed.)

A) Mountain Dental Services is a specialized dental practice whose only service is filling cavities. Mountain has recorded the following for the past nine months: ( answered in2 decimal)

Month	Number of Cavities Filled	Total Cost
January	450	$5,250
February	575	6,250
March	700	6,500
April	300	5,300
May	500	5,950
June	350	5,300
July	600	5,600
August	675	6,500
September	425	5,200

Required:

1. Use the high-low method to estimate total fixed cost and variable cost per cavity filled.

2. Using these estimates, calculate Mountain’s total cost for filling 400 cavities.

B) Riverside Inc. makes one model of wooden canoe. Partial information for it follows: (answered in 2 decimal)

Number of Canoes Produced and Sold
		495		645		795
Total costs
Variable costs	$	71,280		?		?
Fixed costs		149,600		?		?
Total costs	$	220,880		?		?
Cost per unit
Variable cost per unit		?		?		?
Fixed cost per unit		?		?		?
Total cost per unit		?		?		?

Required:

1. Complete the table.

3. Suppose Riverside sells its canoes for $518 each. Calculate the contribution margin per canoe and the contribution margin ratio.

4. Next year Riverside expects to sell 845 canoes. Complete the contribution margin income statement for the company.

C) Riverside Inc. makes one model of wooden canoe. Partial information for it follows: (answered in 2 decimals)

Number of Canoes Produced and Sold		550			750			900
Total costs
Variable costs	$	110,000		$	150,000		$	180,000
Fixed costs		99,000			99,000			99,000
Total costs	$	209,000		$	249,000		$	279,000
Cost per unit
Variable cost per unit	$	200.00		$	200.00		$	200.00
Fixed cost per unit		180.00			132.00			110.00
Total cost per unit	$	380.00		$	332.00		$	310.00

Riverside sells its canoes for $460 each. Next year Riverside expects to sell 1,000 canoes.

Required:

Complete the Riverside’s contribution margin income statement for each independent scenario. Assuming each scenario is a variation of Riverside’s original data. (Round your unit contribution margin and contribution margin ratio to 2 decimal places (i.e. .1234 should be entered as 12.34%) and all other answers to the nearest dollar amount.)

D) Joyce Murphy runs a courier service in downtown Seattle. She charges clients $0.64 per mile driven. Joyce has determined that if she drives 2,750 miles in a month, her total operating cost is $875. If she drives 3,850 miles in a month, her total operating cost is $1,139.

Required:

1. Using the high-low method, determine Joyce’s variable and fixed operating cost components.

2. Complete the contribution margin income statement for Joyce’s service assuming she drove 1,950 miles last month. (Assume this falls within the relevant range of operations).

D) The following information pertains to the first year of operation for Crystal Cold Coolers Inc.:

Number of units produced		2,900
Number of units sold		2,300
Unit sales price	$	330
Direct materials per unit	$	60
Direct labor per unit	$	50
Variable manufacturing overhead per unit	$	14
Fixed manufacturing overhead per unit ($217,500/2,900 units)	$	75
Total variable selling expenses ($11 per unit sold)	$	25,300
Total fixed general and administrative expenses	$	64,000

Required:

Prepare Crystal Cold’s full absorption costing income statement and variable costing income statement for the year.

Example 2-1. The demand: 50,000 yd3 of mixed-asphalt-paving material during four months (17 weeks of 5 days/week) Cost Factor Site A Site B Average hauling distance 4 miles 3 miles Monthly rental of the site $2,000 $7,000 Cost to set up and remove equipment $15,000 $50,000 Hauling expense $2.75/yd3-mile $2.75/yd3-mile Flagperson Not required $150/day Questions: Which site has the lowest total cost? For the site chosen, when will the contractor start having a breakeven (e.g. after delivering a certain amount of material)? What would be the breakeven amount for the unit price equals to $15, $11.5, and $10? Solution You are encouraged to replicate the approach presented here to solve the question. As we discussed in class, write down every detail will help you think and prevent unintentional mistake. Part 1. Total cost = Fixed cost + Variable cost For site A, Variable cost (hauling cost) = unit produced * unit cost = ____________________,. yd3 * ( _____________________ miles * $ _____________________ / yd3-mile) = $ _____________________ . Do replace the comma symble of thousands with a space, e.g. "10 000" instead of "10,000". Fixed cost = rent + setup + flagperson = $ _____________________ /month * _____________________ months + $ _____________________ + $ ___________________ = $ _____________________ So site A’s total cost = $ _____________________ In the same token, for site B, Variable cost = _____________________ yd3 * ( _____________________ * $ _____________________ /yd3-mile ) = $ _____________________ Fixed cost = rent + setup + flagperson = $ _____________________ /month * _____________________. months + $ _____________________ + $ _____________________ /day * _____________________ days/week * _____________________ weeks = $ _____________________ + $ _____________________+ $ ______________________ = $ _____________________ So site B’s total cost = $ _____________________ <= The contractor will chose site B due to its lower cost. Question 2 of 3 What follows is a fill in the blank question with 10 blanks. Part 2. Now we need to find the breakeven point. As we discussed in class, the contractor will spend 4 months to deliver everything. So we are in fact looking for a specific amount of material to be delivered when the contractor’s revenue equals the total cost of delivering that amount of material. The textbook states that the contractor will sell the material for $12/yd3. Assuming an amount of material, Y yd3, will need to be delivered in order to have a breakeven, then the total cost at that point of time is Fixed cost = $ _____________________ for site B, which is not going to change due to the amount being delivered. Variable cost = unit produced * unit cost = Y yd3 * ( _____________________miles * $ _____________________ /yd3-mile ) = $ _____________________ * Y The revenue at that point = unit sold * unit price = Y yd3 * $ _____________________ /yd3 = $ _____________________ * Y To have a breakeven, the revenue has to equal to the total cost, so $ _____________________ * Y = fixed cost + variable cost = $ _____________________ + $ _____________________ * Y So the amount of material to be delivered, Y = _____________________ yd3 Question 3 of 3 What follows is a fill in the blank question with 3 blanks. Part 3. The same equation, revenue = total cost, can be used here. The only thing changed is the unit price. For unit price = $15 /yd3, the amount of material to be delivered, Y = _____________________yd3 (write down your answer as an integer, e.g. no decimal points) Do note that you might have tried to round off the answer. However, that answer is not correct as it is not enough to reach the breakeven point (the shaded area in the right-hand side). In the same token, for unit price = $11.5 /yd3, the amount of material to be delivered, Y = _____________________ yd3 (write down your answer as an integer). For unit price = $10 /yd3, the amount of material to be delivered, Y = _____________________ yd3 (write down your answer as an integer). Do note that the total amount to be delivered is 50,000 yd3 within four months, which is less than your amount above. What this means is that the two lines just convert too slowly, way behind the total amount required. It also means that the unit price is not enough to cover everything; the contractor will lose money at the end.

1. The average production cost for major movies is 57 million dollars and the standard deviation is 22 million dollars. Assume the production cost distribution is normal. Suppose that 46 randomly selected major movies are researched. Answer the following questions. Round all answers to 4 decimal places where possible.

1. What is the distribution of X? X~ N( , )
2. What is the distribution of x¯? x¯ ~ N( , )
3. For a single randomly selected movie, find the probability that this movie's production cost is between 51 and 56 million dollars.
4. For the group of 46 movies, find the probability that the average production cost is between 51 and 56 million dollars.

2. Suppose the age that children learn to walk is normally distributed with mean 11 months and standard deviation 1.1 month. 18 randomly selected people were asked what age they learned to walk. Round all answers to 4 decimal places where possible.

1. What is the distribution of X? X ~ N( , )  
2. What is the distribution of x¯? x¯ ~ N( , )
3. What is the probability that one randomly selected person learned to walk when the person was between 10 and 12.5 months old?
4. For the 18 people, find the probability that the average age that they learned to walk is between 10 and 12.5 months old.
5. For part d), is the assumption that the distribution is normal necessary? Yes or No
6. Find the IQR for the average first time walking age for groups of 18 people.
   Q1 = ______ months
   Q3 = ______ months
   IQR: ______ months

3. The average number of miles (in thousands) that a car's tire will function before needing replacement is 72 and the standard deviation is 12. Suppose that 8 randomly selected tires are tested. Round all answers to 4 decimal places where possible and assume a normal distribution.

1. What is the distribution of X? X ~ N( , )
2. What is the distribution of x¯? x¯ ~ N( , )
3. If a randomly selected individual tire is tested, find the probability that the number of miles (in thousands) before it will need replacement is between 78.2 and 84.2.
4. For the 8 tires tested, find the probability that the average miles (in thousands) before need of replacement is between 78.2 and 84.2.

4. The lengths of adult males' hands are normally distributed with mean 188 mm and standard deviation is 7.2 mm. Suppose that 17 individuals are randomly chosen. Round all answers to 4 decimal places where possible.

1. What is the distribution of x¯? x¯ ~ N( , )
2. For the group of 17, find the probability that the average hand length is more than 187.
3. Find the third quartile for the average adult male hand length for this sample size.

5. Suppose that the average number of Facebook friends users have is normally distributed with a mean of 125 and a standard deviation of about 55. Assume fourteen individuals are randomly chosen. Answer the following questions. Round all answers to 4 decimal places where possible.

1. What is the distribution of x¯? x¯ ~ N( , )
2. For the group of 14, find the probability that the average number of friends is less than 107.
3. Find the first quartile for the average number of Facebook friends

6. The amount of syrup that people put on their pancakes is normally distributed with mean 57 mL and standard deviation 9 mL. Suppose that 41 randomly selected people are observed pouring syrup on their pancakes. Round all answers to 4 decimal places where possible.

1. What is the distribution of X? X ~ N( , )
2. What is the distribution of x¯? x¯ ~ N( , )
3. If a single randomly selected individual is observed, find the probability that this person consumes is between 57.7 mL and 59.2 mL.
4. For the group of 41 pancake eaters, find the probability that the average amount of syrup is between 57.7 mL and 59.2 mL

Do some research online and find 3 cars you are thinking of buying (ranging from low budget, to mid-budget, to one that is your dream car). Find their prices and how many miles per gallon they get

Car A: $26,793 28MPG

Car B: $39,735 17MPG

Car C: $161,139 13PMG

Suppose that you plan on using the car for 100,000 miles . Also let’s assume that all the cars have about the same overall cost of maintenance (just to simplify so you don't have to figure that into your calculations).

• The major uncertainty that you need to entertain is the price of gas in the future. You guess that there are roughly 4 options, given peak oil production and a tailing-off of global oil resources within the next 40 years (gas is a finite resource, in other words): 1) gas at $3 per gallon; 2) at $4; 3) at $5; 4) at $8. This is your partition, your states of affairs.

• The courses of action you may take are the three choices you have for your cars.

• The utilities you assign to your options are the respective price of each car plus the cost of gas for a “lifetime.”

a) Draw a table that lists the states of affairs across the top, and the choices/cars down the left side.

b) Work out the cost of gas for each car over its lifetime given the respective mpg, then fill in the utility of each choice (gas

plus cost of car) in each state of affairs. [40pts]

c) According to the table, is there an option that “dominates” the others? (Remember, in this example domination is about the lowest overall price.) In other words, is there a state of affairs in which one choice of car has costs lower than all the others AND in no other state of affairs does that choice of car cost more than any of the others? Briefly explain your answer and what that answer means.

d) Go back to the table you made in b). Attach the following probabilities to the gas prices over the lifetime of your car: 1) Pr($3)=50%; 2) Pr($4)=40%; 3) Pr($5)=8%; 4) Pr($8)=2%. Compute the expected value of each choice with these probability assignments, and then assess whether there is a value that dominates the others. Briefly explain your answer and what it means.