PART A
A metallic spherical thin shell of radius 0.1 m is charged with a negative charge of 1 μC
a) With what minimum initial velocity should I launch an electron from very far
away so that it can reach the surface of the spherical shell?
b) With what minimum initial velocity should I launch a proton from very far
away so that it can reach the surface of the spherical shell?
c) What is the value of the electric field close to the surface of the shell?
d) If this shell is then put in contact through an electrical wire with another
metallic spherical thin shell of radius 0.05 m which is far away from the first
one and initially discharged, what will be the new value of the electric field near
the surface of the first shell?
e) What will be the value of the electric field near the surface of the second shell?
f) What are the energies of the configurations of charges before and after
connecting the two spheres with the wire
PART B
g) Imagine that the wire used in part d) to connect both spheres does not have a
negligible resistance and has instead a resistance of 1000 W . How would the
answers to d) ,e,) and f) change?
h) Explain in words what would be the difference between both cases.
PART C
i) Remove the wire connecting to the smaller sphere ( which is far away) and
just concentrate on the larger sphere .
j) Draw the magnitude of electric field as a function of the distance from the
center of that sphere. What is the value of that electric field at the following
distances from the center ( 0.2 m , 0.3 m, 0.4 m, )
k) Place a surrounding metallic hollow sphere of inner radius 0.25 m and outer
radius 0.35 m centered at the same point where your original sphere is. That
sphere is given a total charge of + 0. 8 μC.. but not connected or touching in
any way the original sphere. What is the value now at the same distances from
the center ( 0.2 m , 0.3 m, 0.4 m)?
l) What are the charges in the inner and outer surfaces of the hollow sphere?

Can you help me with part b and c

The Mountain Red Vineyard (MRV) is planning to launch a luxury wine brand, MRV Shiraz to be sold at the fixed price ? = ? per barrel. The MRV operations research analyst conducted the

survey of MRV customers and obtained the discrete probability distribution of annual demand for the new luxury wine brand as shown in the table below.

(?)

Further the analyst developed the risk analysis simulation scenario assuming the MRV Shiraz sold quantity is a random variable with discrete probability distribution shown in the table below.

0

3

(?)

The risk analysis simulation scenario also included the fixed cost ? = $300 per barrel of the MRV Shiraz. This cost is associated with introduction and operation of the new production line.

The MRV is committed to have enough supply to meet the demand. The profit function is ? = ? × ? − ? × ?.

Name the Excel sheet ‘Problem 3’.

enter ? = ? of your choice into the cell $B$4;0

Set the input parameter values:

figure below.

0

enter ? = $300 into the cell $B$5.
Your implementation of the simulation model should also include the information shown in the

Let N be the sample size.

1) Could we use a single standard uniform random variable (e.g. to be generated in column B) for simulation of ‘Demand’ and ‘Sold’ quantities instead of two standard uniform random variables? Provide your reasoning.

2) Let ? = 50. Report the average profit and standard deviation of the profit. Construct a 95% - confidence interval for the expected profit using your simulation results.

3) Let ? = 500. Report the average profit and standard deviation of the profit. Construct a 95% - confidence interval for the expected profit using your simulation results.

4) Comment on the tendency of the 95% - confidence intervals obtained in 2) and 3). Explain your answer.

4

5) Give a ‘break-even’ price estimate, you would recommend to the MRV operations research analyst, using your simulation results. Give your reasoning.

Five years ago, a company was considering the purchase of 68 new diesel trucks that were 14.63% more fuel-efficient than the ones the firm is now using. The company uses an average of 10 million gallons of diesel fuel per year at a price of $1.25 per gallon. If the company manages to save on fuel costs, it will save $1.875 million per year (1.5 million gallons at $1.25 per gallon). On this basis, fuel efficiency would save more money as the price of diesel fuel rises (at $1.35 per gallon, the firm would save $2.025 million in total if he buys the new trucks).

Consider two possible forecasts, each of which has an equal chance of being realized. Under assumption #1, diesel prices will stay relatively low; under assumption #2, diesel prices will rise considerably. The 68 new trucks will cost the firm $5 million. Depreciation will be 25.49% in year 1, 38.5% in year 2, and 36.35% in year 3. The firm is in a 39% income tax bracket and uses a 9% cost of capital for cash flow valuation purposes. Interest on debt is ignored. In addition, consider the following forecasts:

Forecast for assumption #1 (low fuel prices):

Required: Calculate the percentage change on the basis that an increase would take place from the NPV under assumption #1 to the probability-weighted (expected) NPV.

Probability of getting 3 in a single toss of die =

aw of addition: page 168

1. In a manufacturing line there are several operations to produce a component. The probability of getting a surface finish defect on operation-10 is 2/3and probability of getting a dimensional defect on operation-20 is 5/9.After manufacturing finished components,

1. what is the probability of getting a surface finish defect?

2. what is the probability of NOTgetting at least one surface finish defect?

Probability of an event A is P(A) and its complement is Ā. P(A)+P(Ā)=1  or P(Ā) = 1 - P(A)

3. what is the probability of getting both type of defects in the finished component?

If A and B are independent events, the probability that both A and Bwill occur is

P(AB) = P(A∩B) = P(A) x P(B)

4. probability of either surface finish defect ordimensional defect in the finished product is

P(A U B) = P(A) + P(B) – P(A∩B) =

Law of multiplication:

2. In one shift, the probability of tool change on operation 10, P(A) is 0.6. The probability of tool change on operation 20, P(B) is 0.5. The probability of tool change on both operations 10 and 20, P(A∩B) is 0.3.

Note: The tool change on operations are independent.

P(A) = 0.6, P(B) = 0.5 and P(A∩B) = 0.3

Independent:P(AB) = P(A∩B) = P(A) x P(B)

The probability of tool change on both operations 10 and 20

P(A∩B)  = P(A) x P(B) =

The probability of tool change on eitheroperation 10 or 20

P(A) or  P(B) = P(A U B) =

3. The probability of three independent machines on an assembly line with failures are as follows:

P(A failing) = 0.15, P(B failing) = 0.05, P(C failing) = 0.10

1. What is the probability of all three machine work?

Independent failures:

P(A failing) = 0.15,  P(A NOT failing) =

P(B failing) = 0.05, P(B NOT failing) =

P(C failing) = 0.10, P(C NOT failing) =

Probability of all three machines work =

2. What is the probability of the assembly line fail (NOT work)?

Assume you are the marketing manager of a large electronic equipment manufacturing firm. It is the Spring of the year 2004. Your firm has pioneered an electronic book reader that mimics the reading experience on paper and the test-market results have indicated that the new product will be well received. However, as it is a completely new product on the market, the firm is unsure of adoption rates. You are in charge of a large geographical region in Asia and a third-party market research firm has indicated that the total market size is likely to be 280 million. The task of developing a reliable forecast now rests on your shoulders and you decide to put the learnings from your NPD class to work. As you do not have previous sales information to forecast, you decide to use a bass model based prediction by analogy.

There are two analogous products with their respective precalculated coefficients of innovation (p) and imitation (q). However, you decide to rate the products based on three factors using experts on a 10-point scale in order to use a weighted average technique to determine the final p and q to use. The following table shows the relevant numbers.

Given the information you have, what is the final coefficient of innovation you’d use to compute forecasts using the Bass model by analogy?

What is the final coefficient of imitation you’d use to compute forecasts using the Bass model by analogy?

Using those p and q suggested by the weighted average technique, and market size = 280 million, what will be your forecast of new product adoption for the first year (2004)?

What will be your sales forecast in millions for the year 2006 (third year from launch assuming the same parameters as in previous question)

When will the cumulative sales exceed 50 million units?

In the year 2006, how much of the total annual sales in millions can be attributed to the effect of imitation instead of innovation?

Consider a family with a mother, father, and two children. Consider the following set of events: A1 = {mother has influenza} A2 = {father has influenza} A3 = {first child has influenza} A4 = {second child has influenza} B = {at least one child has influenza} C = {at least one parent has influenza} D = {at least one family member has influenza}

1. What does A1 ∪ A2 mean? Which answer is correct? Please provide explanation

2. Are A3 and A4 mutually exclusive events? Which answer is correct? Please provide explanation

a. Yes

b. No

c. Maybe

3. Express D in terms of B and C. Which answer is correct? Please provide explanation

Suppose an influenza epidemic strikes a city. In 10% of families, the mother has influenza. In 10% of families, the father has influenza. In 2% of families, both the mother and father have influenza. Furthermore, suppose each child has a 20% chance of contracting influenza and there is a 10% chance both children become diseased.

4. Considering the set of events from Question 5, are A1 and A2 independent? Which answer is correct? Please provide an explanation.

a. Maybe

b. Yes

c. No

5. What is the probability that at least one child will get influenza? Which answer is correct? There might be slight rounding differences. Please provide an explanation.

a. 0.2

b. 0.5

c. 0.3

d. 0.1

6. Based on your result from Part (a), what is the conditional probability that the father has influenza given the mother has influenza? Which answer is correct? There might be slight rounding differences. Please provide an explanation.

a. 0.5

b. 0.2

c. 0.3

d. 0.1

I need a paragraph analysis/summaryhe results of this income statement using the indirect method.

Scenario: Imagine you are a researcher who is interested in studying whether sleep deprivation leads to increased reaction times (i.e., being slower) when driving. You randomly select a sample of 30 licensed drivers. Fifteen participants are randomly assigned to get 5 hours of sleep for three consecutive nights. The other 15 participants are randomly assigned to get 8 hours of sleep for three consecutive nights. For the purposes of this Assignment, assume that all participants sleep exactly the required amounts. After the third night, all participants take a driving simulation test that measures their reaction times.

Use SPSS to determine if amount of sleep is related to reaction time.

1. Explain whether the researcher should use an independent-samples t-test or a related-samples t-test for this scenario. Provide a rationale for your decision.
2. Identify the independent variable and dependent variable.
3. Knowing the researcher believes that people who sleep less will have slower reaction times, state the null hypothesis and alternate hypothesis in words (not formulas).
4. Explain whether the researcher should use a one-tailed test or two-tailed test and why.
5. Identify the obtained t value for this data set using SPSS and report it in your answer document.
6. State the degrees of freedom and explain how you calculated it by hand.
7. Identify the p value using SPSS and report it in your answer document.
8. Explain whether the researcher should retain or reject the null hypothesis. Provide a rationale for your decision. Are the results statistically significant?
9. Explain what the researcher can conclude about the relationship between amount of sleep and reaction times.

Data:

Reaction times in seconds for participants with 5 hours of sleep
0.22
0.25
0.27
0.25
0.24
0.28
0.24
0.3
0.25
0.21
0.28
0.23
0.29
0.25
0.29

Reaction times in seconds for participants with 8 hours of sleep
0.21
0.23
0.2
0.24
0.28
0.23
0.3
0.29
0.23
0.21
0.21
0.27
0.29
0.23
0.25

1. A small mattress company recently started its operations and currently does not have enough resources to utilize high-tech forecasting software. The manager wants to utilize traditional methods of forecasting to estimate demand. The following recent data on monthly sales are available from the past year. Use this information to answer the following set of questions.

1. If the manager uses a naïve forecasting method. What is the forecast for Jan 2020? (2 pts.)

1. Use the three-period moving average method and estimate forecast beginning from Aug-19 to Jan-20. Use 0.4, 0.3, and 0.2 as weights with highest weights given to the most recent periods (8 pts.)
   
2. Calculate the Mean Absolute Deviation of forecasts from the three-period moving average. (5 pts.)
   

              2. Use the same date from Q1. to answer the following questions. (10 pts.)

1. Use the exponential smoothing method to calculate forecast from Aug-19 to Jan-20. Use an α value of 0.3.

You need a beginning forecast of Jul-19 to start this. Use the naïve forecast for estimating Jul-19, and then use the answer to start the exponential smoothing method.

(Please show all the work for credit on this. You can use excel too, but show the logic/formula if using excel)

The answers were given for this problem, but I am not sure how to derive them. Would need any kind of help

Suppose that you sell Christmas trees each holiday season for $30 a tree. Peak selling time is the 2 weeks leading up to Christmas, but since harvesting real pine trees takes time, your supplier requires a 1 month lead time.

Your purchase cost per tree is $20. Anytime a customer comes to your store requesting a tree and it is unavailable, you give them a $5 credit (per tree) to spend on other products. (You should assume they always use this credit.) Any trees not sold before Christmas are sold to a local lumber yard at $10/tree.

Demand for this Christmas is forecasted in the following table.

a) (3 points) To the nearest tree, what is the expected demand for this Christmas? (Remember, as with all questions, you should show work for full credit.) 750 trees

b) (3 points) Suppose you order exactly 800 trees, how many trees would you expect to sell? (Remember, as with all questions, you should show work for full credit.) 730 trees

c) (3 points) Suppose you order exactly 800 trees while the actual demand turns out to be 700 trees, what is your expected profit (including goodwill costs if there are any)? $6000

d) (3 points) What is the underage cost? What is the overage cost? Just by comparing the two costs, should we order more or less than the average demand? Briefly explain.

Underage: $15

Overage: $10

We should order more than average, but why? I don't understand the explanation

e) (3 points) What is the optimal order quantity given the demand in part a)? As with all questions, please show work for full credit. 800 trees

f) (1 point) What is the effective service level for the quantity you suggested in part e)? 80%