Rauschenberg Manufacturing is investigating which locations would best position its new plant relative to three important customers​ (located in cities​ A, B, and​ C). As shown in the table​ below, all three customers require multiple daily deliveries. Management limited the search for this plant to those three locations and compiled the following​ information:

a. Which of these three locations yields the smallest​ load-distance score, based on Euclidean​ distances?

Location ____yields the smallest​ load-distance score of _____ ​(Enter your response rounded to one decimal​ place.)

b. Which of these locations is​ best, based on rectilinear​ distances?

Location ____is the​ best, yielding a​ load-distance score of ______​(Enter your response as a whole​ number.)

c. What are the coordinates of the center of​ gravity?

The center of gravity is x*=_____​miles, y*=____miles. ​(Enter your responses rounded to one decimal​ place.)

uide to marks: 20 marks – 12 for a, 2 for b, 6 for c

Tully Tyres sells cheap imported tyres. The manager believes its profits are in decline. You have just been hired as an analyst by the manager of Tully Tyres to investigate the expected profit over the next 12 months based on current data.

•Monthly demand varies from 100 to 200 tyres – probabilities shown in the partial section of the spreadsheet below, but you have to insert formulas to ge the cumulative probability distribution which can be used in Excel with the VLOOKUP command.
•The average selling price per tyre follows a discrete uniform distribution ranging from $160 to $180 each. This means that it can take on equally likely integer values between $160 and $180 – more on this below.
•The average profit margin per tyre after covering variable costs follows a continuous uniform distribution between 20% and 30% of the selling price.
•Fixed costs per month are $2000.

(a)Using Excel set up a model to simulate the next 12 months to determine the expected average monthly profit for the year. You need to have loaded the Analysis Toolpak Add-In to your version of Excel. You must keep the data separate from the model. The model should show only formulas, no numbers whatsoever except for the month number.

You can use this partial template to guide you:

The first random number (RN 1) is to simulate monthly demands for tyres.
•The average selling price follows a discrete uniform distribution and can be determined by the function =RANDBETWEEN(160,180) in this case. But of course you will not enter (160,180) but the data cell references where they are recorded.
•The second random number (RN 2) is used to help simulate the profit margin.
•The average profit margin follows a continuous uniform distribution ranging between 20% and 30% and can be determined by the formula =0.2+(0.3-0.2)*the second random number (RN 2). Again you do not enter 0.2 and 0.3 but the data cell references where they are located. Note that if the random number is high, say 1, then 0.3-0.2 becomes 1 and when added to 0.2 it becomes 0.3. If the random number is low, say 0, then 0.3-0.2 becomes zero and the profit margin becomes 0.2.
•Add the 12 monthly profit figures and then find the average monthly profit.

Show the data and the model in two printouts: (1) the results, and (2) the formulas. Both printouts must show the grid (ie., row and column numbers) and be copied from Excel and pasted into Word. See Spreadsheet Advice in Interact Resources for guidance.

(b)Provide the average monthly profit to Ajax Tyres over the 12-month period.

(c)You present your findings to the manager of Ajax Tyres. He thinks that with market forces he can increase the average selling price by $40 (ie from $200 to $220) without losing sales. However he does suggest that the profit margin would then increase from 22% to 32%.

He has suggested that you examine the effect of these changes and report the results to him. Change the data accordingly in your model to make the changes and paste the output in your Word answer then write a report to the manager explaining your conclusions with respect to his suggestions. Also mention any reservations you might have about the change in selling prices.

The report must be dated, addressed to the Manager and signed off by you.
(Word limit: No more than 150 words)

Tully Tyres sells cheap imported tyres. The manager believes its profits are in decline. You have just been hired as an analyst by the manager of Tully Tyres to investigate the expected profit over the next 12 months based on current data.

•Monthly demand varies from 100 to 200 tyres – probabilities shown in the partial section of the spreadsheet below, but you have to insert formulas to ge the cumulative probability distribution which can be used in Excel with the VLOOKUP command.
•The average selling price per tyre follows a discrete uniform distribution ranging from $160 to $180 each. This means that it can take on equally likely integer values between $160 and $180 – more on this below.
•The average profit margin per tyre after covering variable costs follows a continuous uniform distribution between 20% and 30% of the selling price.
•Fixed costs per month are $2000.

(a)Using Excel set up a model to simulate the next 12 months to determine the expected average monthly profit for the year. You need to have loaded the Analysis Toolpak Add-In to your version of Excel. You must keep the data separate from the model. The model should show only formulas, no numbers whatsoever except for the month number.

The first random number (RN 1) is to simulate monthly demands for tyres.
•The average selling price follows a discrete uniform distribution and can be determined by the function =RANDBETWEEN(160,180) in this case. But of course you will not enter (160,180) but the data cell references where they are recorded.
•The second random number (RN 2) is used to help simulate the profit margin.
•The average profit margin follows a continuous uniform distribution ranging between 20% and 30% and can be determined by the formula =0.2+(0.3-0.2)*the second random number (RN 2). Again you do not enter 0.2 and 0.3 but the data cell references where they are located. Note that if the random number is high, say 1, then 0.3-0.2 becomes 1 and when added to 0.2 it becomes 0.3. If the random number is low, say 0, then 0.3-0.2 becomes zero and the profit margin becomes 0.2.
•Add the 12 monthly profit figures and then find the average monthly profit.

Show the data and the model in two printouts: (1) the results, and (2) the formulas. Both printouts must show the grid (ie., row and column numbers) and be copied from Excel and pasted into Word. See Spreadsheet Advice in Interact Resources for guidance.

(b)Provide the average monthly profit to Ajax Tyres over the 12-month period.

(c)You present your findings to the manager of Ajax Tyres. He thinks that with market forces he can increase the average selling price by $40 (ie from $200 to $220) without losing sales. However he does suggest that the profit margin would then increase from 22% to 32%.

He has suggested that you examine the effect of these changes and report the results to him. Change the data accordingly in your model to make the changes and paste the output in your Word answer then write a report to the manager explaining your conclusions with respect to his suggestions. Also mention any reservations you might have about the change in selling prices.

The report must be dated, addressed to the Manager and signed off by you.
(Word limit: No more than 150 words)

1. Suppose you are in the market for a new car. You identify two models that you like and are considering a final purchase decision. The vehicle details are as follows:

• One is a high fuel efficient vehicle with a fuel cost per mile of $0.10 and the other is a low fuel efficient vehicle with a fuel cost per mile of $0.15.
• The high efficiency vehicle costs $47,500 in time period 0 (no discounting); the low efficiency vehicle costs $32,500
• You plan to drive the car for five years (time periods 1 to 5)
• In addition to the fuel costs in period 5, you also face depreciation costs of $17,500 for the low efficient vehicle and depreciation costs of $40,000 for the high efficient vehicle

1. 1. Suppose you drive 10,000 miles per month and have an internal discount rate of 5%. Which car has the lower total cost of ownership? Show your work on a separate page or attach a printout of your excel model, clearly labeled.
2. 2. Suppose you drive 17,000 miles per month and have an internal discount rate of 5%. Which car has the lower total cost of ownership? Show your work on a separate page or attach a printout of your excel model, clearly labeled.
3. 3. Suppose you drive 7,500 miles per month and have an internal discount rate of 20%. Which car has the lower total cost of ownership? Show your work on a separate page or attach a printout of your excel model, clearly labeled.
4. 4. In general, what characteristics (in terms of driving habits and discount rates) describe an individual that finds a lower total cost of ownership in high fuel efficient vehicles?

part 1)

A road perpendicular to a highway leads to a farmhouse located 1 mile away. An automobile traveling on the highway passes through this intersection at a speed of 65mph. How fast is the distance between the automobile and the farmhouse increasing when the automobile is 6 miles past the intersection of the highway and the road? The distance between the automobile and the farmhouse is increasing at a rate of miles per hour.

part 2)

A boat is pulled into a dock by means of a rope attached to a pulley on the dock. The rope is attached to the front of the boat, which is 10 feet below the level of the pulley. If the rope is pulled through the pulley at a rate of 20 ft/min, at what rate will the boat be approaching the dock when 110 ft of rope is out?

The boat will be approaching the dock at  ft/min.

Hint: Sketch a diagram of this situation.

part 3)

Oil spilled from a ruptured tanker spreads in a circle whose area increases at a constant rate of 6 mi2/hrmi2/hr. How rapidly is radius of the spill increasing when the area is 10 mi2mi2?

The radius is increasing at  mi/hr.

part 4)

At noon, ship A is 40 nautical miles due west of ship B. Ship A is sailing west at 18 knots and ship B is sailing north at 15 knots. How fast (in knots) is the distance between the ships changing at 6 PM?

The distance is changing at  knots.

(Note: 1 knot is a speed of 1 nautical mile per hour.)

part 5)

A spherical balloon is inflated so that its volume is increasing at the rate of 3.8 ft3/minft3/min. How rapidly is the diameter of the balloon increasing when the diameter is 1.8 feet?

The diameter is increasing at  ft/min.

The US consumer fleet (cars, SUV’s, vans, cross-overs and light trucks) has an average drag coefficient of 0.4, an average miles driven per year of 12,500 at 50 MPH and an average frontal area of 5.5 m2. Being that there are 265 million of these ‘average’ vehicles on the road driven by consumers, calculate:

a. Gasoline consumed per vehicle annually assuming 25% overall efficiency

b. Gasoline consumed per vehicle annually assuming if the speed limit on federal highways was cut down from 70 to 55 MPH resulting in a decrease in the average speed to 43 MPH.

c. How many barrels of oil would be saved annually by lowering the speed limit?

d. If instead of 55 MPH there were an absolute federal speed limit on all roads of 45 MPH, lowering the average speed to 35 MPH, repeat b) and c) above.

e. If instead of lowering the speed limit the aerodynamics of all vehicles were improved such that the average vehicle now has a drag coefficient of 0.35, how many barrels of oil would that save annually?

f. If the size of engines were cut down on every vehicle in the fleet equivalent to the efficiency of the average vehicle above increasing to 40%, how many barrels of oil would that save annually?

g. What if by force of tax we were all limited in driving a certain number of miles and this resulted in the original average vehicle driving 10,000 miles per year, how many barrels of oil would that save annually? How many gallons of gas is that per capita and how much would each person save dollar-wise per year?

9. Let f (x) = x^3 − 10. Find all numbers c in the interval (-11, 11) for which the line tangent to the graph of f is parallel to the line joining (−11, f (−11)) and (11, f(11)). How many such numbers exist in the given interval?

. 0

. 1

. 2 (correct)

. 3

Enter points in increasing order (smallest first). Enter DNE in any empty answer blank.

c =

c =

c = DNE (correct)

10. Let g(x) = x² − (5/x)

First find the slope m of the line joining (1, g(1)) and (2, g(2)). Then use the Newton-Raphson method to estimate the values of c for which g'(c) = m. Check that your calculator is set for at least 10 digit display. Continue the process until successive iterations obtained by the calculator are identical.

m = 0.5 (incorrect)

0

1 (correct)

2

3
Enter values of c below in order from least to greatest. Enter DNE in any empty answer blanks.
c =  
c = DNE (correct)
c = DNE (correct)

11. A landowner wishes to use 15 miles of fencing to enclose an isosceles triangular region of as large an area as possible. What should be the lengths of the sides of the triangle?
Let x be the length of the base of the triangle. Write the area as a function of x. [First write the length of the equal-length sides in terms of the base, x, then write the height of the triangle in terms of the base.]

A(x) =_______________

Length of base = ____________ miles

Length of the other two (equal-length) sides = ______________ miles each

On

January

1​,

2018​,

On Time

Delivery Service purchased a truck at a cost of

$75,000.

Before placing the truck in​ service,

On Time

spent

$2,200

painting​ it,

$1,700

replacing​ tires, and

$9,100

overhauling the engine. The truck should remain in service for five years and have a residual value of

$10,000.

The​ truck's annual mileage is expected to be

27,000

miles in each of the first four years and

12,000

miles in the fifth

year—120,000

miles in total. In deciding which depreciation method to​ use,

Jacob Nealy​,

the general​ manager, requests a depreciation schedule for each of the depreciation methods​ (straight-line, units-of-production, and​ double-declining-balance).Read the requirements

LOADING...

.

Requirement 1. Prepare a depreciation schedule for each depreciation​ method, showing asset​ cost, depreciation​ expense, accumulated​ depreciation, and asset book value.

Begin by preparing a depreciation schedule using the​ straight-line method.

Part I

Find the standard-normal curve area that lies a)To the right of 0.65 b) To the left of z = -2.13 c) between z = -0.34 and z = 0.62.

d) A tire store finds that the thread life of its tires is normally distributed, with a mean of 26,640 miles and a standard deviation of 4000 miles. The store sold 9000 tires this month. How many of them can be expected to last between 25,000 and 30,000 miles?

Part II 15

a)From a random sample of 36 business days , the average closing price of Apple Stock was $116.16 with a standard deviation of $10.27. Construct a 90% and 95% confidence interval. Which interval is wider?

b) Determine the minimum sample size required   when you want to be 95% confident that the sample mean is within one unit of the population mean and σ=4.8.(population standard deviation)

Part III (Hypothesis testing )

A company that makes cola drinks states that the mean caffeine content per 12-ounce bottle of cola is 40 milligrams. You want to test this claim. During your tests, you find that a random sample of twenty 12 ounce-bottles of cola has a mean caffeine content of 39.2 milligrams. Assume the population is normally distributed and the population standard deviation is 7.5 milligram. At α = .01, can you reject the company’s claim?

1. Identify the claim. State the null and alternative hypotheses
2. Identify the level of significance , the critical value and the direction of the test
3. Find the standardized test statistic z.
4. Construct the rejected region and decide whether to reject the Null Hypothesis.
5. Find the p-value
6. Interpret the result in the context of the original claim

1. High-Low Method for a Service Company

Boston Railroad decided to use the high-low method and operating data from the past six months to estimate the fixed and variable components of transportation costs. The activity base used by Boston Railroad is a measure of railroad operating activity, termed “gross-ton miles,” which is the total number of tons multiplied by the miles moved.

Determine the variable cost per gross-ton mile and the fixed cost.

2.

Contribution Margin and Contribution Margin Ratio

For a recent year, Wicker Company-owned restaurants had the following sales and expenses (in millions):

Assume that the variable costs consist of food and packaging, payroll, and 40% of the general, selling, and administrative expenses.

a. What is Wicker Company's contribution margin? Round to the nearest million. (Give answer in millions of dollars.)
$ _______million

b. What is Wicker Company's contribution margin ratio? Round to one decimal place.
_______ %

c. How much would income from operations increase if same-store sales increased by $2,100 million for the coming year, with no change in the contribution margin ratio or fixed costs? Round your answer to the closest million.
$ ________ million