Equipment Favorable Market $ Unfavorable Market$

K Brown is the principal owner of Brown oil inc, after quitting his university teachihng job, ken has been able to increase his annual salary by a factor of over 100. at the present time, ken is forced to consider purchasing some more equipment for brown oil because of competition. His alternatives are showing in the following table:

Equipment Favorable Market $ Unfavorable Market$

Sub 100 300,000 -200,000

Oiler J 250,000 -100,000

Texan 75,000 -18,000

For ex, if ken purchases a Sub 100 and if there is a favorable market he will realize a provit of 300,000. On the other hand if the market is unfavorable ken will suffer a loss of 200,000. But ken has alwasy been very optimistic decison maker

a)  what type of decision is Ken facing

Decision under uncertainty

b)  what decison criterion should he use?

Maximax

c)  what alternative is best

He should choose Sub100, since it has the best possible outcome.

2) although Ken (above) is the principal owner, his bother bob is credit with making the company a sucess. Bob is vice president of fincance. Bob attributes his sucess to hsi pessimistic attitude about business and oil industry. Give the information from the previous problem is it likely bob will arive at a different decision? What deicison criterion should bob use, and what alternative will he select?

He should use the minimax regret criterion, minimizing the worst-case scenario. He would select Texan

3) Megley cheese company is a small manu. of several chees products. On of the producst is a cheese spread. That is sold in reail outlets. jason must decide home many cases of cheese spread to manufacture each month. The probabily that the demand will be 6 case is 0.1 for 7 cs is 0.3 for 8 cs is 0.5 and 9 cs is 0.1. the cost of ever case is $45 adn the price that jason gets for each case is $95. Unfortunately any cases not sold by the end of the month are of no vaule cus the spoil. Home cases of cheese should janson manufacture each month?

Cost / 45
Revenue / 95
PRODUCED / COST / PRODUCED / COST / PRODUCED / COST / PRODUCED / COST
6 / 270 / 7 / 315 / 8 / 360 / 9 / 405
Demand / profit / Expected profit / profit / Expected profit / profit / Expected profit / profit / Expected profit
6 / 0.1 / 300 / 30 / 255 / 25.5 / 210 / 21 / 165 / 16.5
7 / 0.3 / 300 / 90 / 350 / 105 / 305 / 91.5 / 260 / 78
8 / 0.5 / 300 / 150 / 350 / 175 / 400 / 200 / 355 / 177.5
9 / 0.1 / 300 / 30 / 350 / 35 / 400 / 40 / 450 / 45
TOTAL / 300 / 340.5 / 352.5 / 317

Producing 8 cases provides the highest total expected profit ($352.50)

the operations manager of a musical instrument distributor feels that demand for bass drums may be related to the number of tv apperances by the popular rock group Green Shades. During the preceeding month. The manager has collected the data to show on the following table

Demands for Bass Drums Green Shades TV appearnaces

3 3

6 4

7 7

5 6

10 8

8 5

a) graph these data to see whether a linear equation migh describe the relationship between the groups television show and bass drum sales.

b) using the equations presented in this chapter comput the SST, SSE and SSR. Find the least squares regression line for this data.

SSR =

(4-3)^2 + (5-6)^2 + (8-7)^2 + (7-5)^2 + (9-10)^2 + (6-8)^2 =

1 + 1 + 1 + 4 + 1 + 4 =

12

SSE =

(4-6.25)^2 + (5-6.25)^2 + (8-6.25)^2 + (7-6.25)^2 + (9-6.25)^2 + (6-6.25)^2 =

6.25 + 2.25 + 2.25 + 0.25 + 6.25 + 0.25 =

17.5

SST = SSR + SSE

SST = 12 + 17.5 = 29.5

Regression line: y = x + 1

C what is your estimate for bass drum sales if the green shades perfomed on tv 6 times last month?

y = x + 1

y = 6 + 1

y = 7

2)Studens in a mangemnt science clas have jsut received grades ona first test. The instructor has provided info about the first test grades in some previous classes as well as the final average for the same students. Some of the grades have been samples as follows:

Student 1 2 3 4 5 6 7 8 9

1st tst gd 98 77 88 80 96 61 66 95 69

Final avg 93 78 84 73 84 64 64 95 76

A)  develop a regresssion model that could be used to predict the final average in the course based on the first test grade

b) predict the final average of a student who made an 83 on the fist test

y = 0.7399x + 18.989

y = 0.7399(83) + 18.989

y = 80.40

c) give values of r and r2 for this model. Interpret the value of r2 in the context of the problem

r2 = 0.8474

r = sqrt(0.8474) = 0.92054

84% of the variance in the second exam score is explained by the first exam score.

3)Accountatns at the firm walker and walker believed that several travleing executives submit unusualy high travel voucherswhen they return from trips. The accounts. took a smaple of 200 vouchs sumbited last year the then developed the following mulitiple regression equation relating expected travel cost (Y) to number days on the road (X1) and distance traveled (X2) in miles:

y= $90,000+$48.50X1+$0.40X2

The coefficient of correlation computed was 0.68.

a)  if thomas williams returns form a 300 mile trip that took him of of town for 5 days, what is the expected amount that he should claim as expenses?

y= $90+$48.50(5)+$0.40(300)

y = $452.50

b)  williams submitted a reimbursement request for $685 what should the accountant do?

The accountant should calculate a 95% prediction interval for the regression model, and see whether or not $685 falls within it. If not, then the accountant can be 95% certain that Williams’ expenses are too high, based on the current model. This does not necessarily mean that Williams has submitted a fraudulent report, as there may be another common cause.

c) comment on the vailidit of this model/. Should any other variable be included? Which ones? Why

If the correlation coefficient is 0.68, then the model is moderately valid. One possible variable might include a cost-of-living index for the city visited. The model could also be divided into trips that do/do not include airfare (or perhaps trips over/under 100 miles, which could substitute). A driving trip might be expected to cost less than an air trip under most circumstances.