Final Exam Review-1 PDF

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Final Exam Review

This document is for review purposes and does not represent every type of problem that may be on the QMB3600 cumulative final exam.

Probability Concepts 1.

This problem is about students who may or may not take advantage of the opportunities provided in QMB such as homework. Some of the students pass the course, and some of them do not pass. Research indicates that 40% of the students do the assigned homework. Of the students who do homework, there is an 80% chance they will pass the course. The probability of not passing if the student does not do the homework is 90%. What is the probability of a student not doing homework or passing? A. B. C. D. E.

2.

.32 .52 .94 .92 .38

Suppose that for a certain football game the probability that the home team will be ahead at half time is 0.60. The probability that the home team will be ahead at half time and also win the game is 0.45. What is the probability that the home team will win this game given that it is ahead at half time? A. B. C. D. E.

.45 .75 .15 .27 None of the above.

1

3.

A company markets two products (Product A and Product B) through mail order. The company will market them in sequence with the first mail order offer for product A. There is a 30% chance that any customer will purchase product A. Product B is offered some months later. It is felt, for product B, that there is a 30% chance of selling product B to a customer if the customer purchased product A and a 5% chance of selling product B to a customer who did not purchase product A. What is the probability of not selling product B to a customer? A. B. C. D. E.

4.

A quality control department finds that it accepted only 5% of all bad items and it rejected only 1% of good items. A supplier has just delivered a shipment of a certain item. Past records show that only 90% of the parts of that supplier are good. If the department accepts an item, what is the probability that the item is bad? Round your answer to five decimal places. A. B. C. D. E.

5.

.875 .665 .125 .210 None of the above

0.05000 0.00558 0.35714 0.09635 None of the above

The probability that house sales will increase over the next six months is estimated at 0.25. It is also estimated that the probability is 0.74 that 30 year fixed-loan mortgage rates will increase over this period. Economists estimate that the probability is 0.89 that either housing sales or interest rates will increase. The probability that both house sales and interest rates will increase is estimated at: A. B. C. D. E.

.100 .185 .705 .900 .500

2

Use the following information to answer the next three questions:

6.

In a survey about soft drinks it was found that 5% of the respondents like diet soft drinks. 12% of all respondents liked the brand Coke. Of all the Diet soda drinkers 40% liked Coke. What is the probability that a respondent likes Coke and Diet drinks? A. B. C. D. E.

7.

What is the probability that the respondent likes Diet or Not Coke? A. B. C. D. E.

8.

.03 .93 .90 .74 .88

Of the people who did not like diet drinks what is the probability that they liked Coke? A. B. C. D. E.

9.

.12 .40 .17 .02 .15

.1053 .1000 .0950 .9500 .1200

Over the last 100 business days, Harry had 20 customers on 30 of those days, 25 customers on 20 days, 35 customers on 30 days, 40 customers on 10 days, and 45 customers on 10 days. What is the variance of the number of Harry’s customers? Hint: Use the Test 1 Formula Sheet for Variance. A. B. C. D. E.

30 38 59 75 83

3

Probability Distributions 10.

What is the probability that exactly 1 out of 10 cars experience a breakdown if the probability of a breakdown is 30%? Assume a Binomial distribution. A. B. C. D. E.

11.

.5121 .1211 .0282 .3828 .4276

An accounts receivable auditor is examining accounts for a client. The accounts receivable balance can be considered as a continuous random variable that exhibits normal distribution characteristics. The mean amount due per account is 5000. The standard deviation is $1000. The auditor selects an account at random. Determine the probability that the account selected by the Auditor has a balance which is outside of the range between $6500 and $7000: A. B. C. D. E.

12.

.05 .10 1.20 .96 .00

Suppose the length of time (in days) between sales for an automobile salesperson is modeled as an exponential distribution with a mean of 2 days. What is the probability the salesperson goes more than 5 days without a sale? A. B. C. D. E.

.75 .92 .08 .40 None of the above.

4

13.

During lunch time, customers arrive at Joe’s Lunch counter according to a Poisson distribution with an average of 2 per 30 second period. What is the probability of having more than two arrivals in a two-minute period? A. B. C. D E.

.9862 .9970 .0027 .7619 None of the above

Decision Theory Use the following scenario to answer the next two questions. The new owner of a beauty shop is trying to decide whether to hire one, two, or three beauticians. She estimates that profits next year (in thousands of dollars) will vary with demand for her services and has estimated demand in three categories low, medium and high.

Number Of Beauticians One Two Three

14.

Low 50 0 100

Medium 75 100 70

High 100 100 300

If she uses the optimistic criterion, how many beauticians will she decide to hire? A. B. C. D. E.

15.

Demand

one two three either one or two either two or three

If she uses the minimax regret criterion, how many beauticians will she decide to hire? A. B. C. D. E.

one two three either one or two either two or three 5

Use the payoff table below to answer the next two questions. 0.2 S1 500 600 -100

D1 D2 D3

16.

0.1 S3 -400 200 900

Determine the expected value for the best decision. A. B. C. D. E.

17.

0.7 S2 300 200 -300

280 137 410 270 -140

Determine the most you would pay for a highly reliable forecast. A. B. C. D. E.

280 10 420 140 -140

6

Use the following decision tree to respond to the next 5 questions: Low Demand .75 Small Store Survey Shows Low Demand P=.60

6

3 Large Store

Survey

7

30

High Demand .25

50

Low Demand .75

10

High Demand .25

80

2 Low Deman .125 Small Store

1 Survey Shows High Demand P=.40

8

4

Low Deman .125 Large Store

No Survey

High Deman .875

9

High Demand .875 Low Demand .50

Small Store

5

Low Demand .50

18.

What is the expected value at node 4? A. 47.50 B. 43.75 C. 70.00 D. 45.00 E. 71.25

19.

What is the expected value of perfect information? A. 45.00 B. 40.00 C. 10.00 D. 5.00 E. 49.25 7

50 10 80 30

10

High Demand .50

Large Store

30

50 10

11 High Demand .50

80

20.

What is the expected value at node 2? A. B. C. D. E.

21.

What is the expected value of sample information? A. B. C. D. E.

22.

35.00 7.50 47.50 49.50 55.00

45.00 71.25 49.50 1.25 4.50

What is the efficiency rating? A. B. C. D. E.

1 .45 .09 .22 1.1

8

Regression and Forecasting Use the output below to answer the next two questions. SUMMARY OUTPUT Regression Statistics Multiple R

0.92

R Square

0.85

Adjusted R Square Standard Error

0.83 4.38

Observations Analysis of Variance

10

Regression

df 1

SS 890.19

Residual

8

153.41

Total

9

1043.59

Coefficients

Standard Error

29.73

2.99

3.28

0.48

Intercept Factory-Fitted

23.

Predict the delivery time for a car with 10 options. A. B. C. D. E.

24.

32.80 3.070 62.53 43.01 -3.070

A statistician working for a car manufacturer developed a statistical model for predicting delivery time (the number of days between ordering a car and actual delivery) of a particular model for which there is a range of factory-fitted options. Forecast the difference in delivery times for cars with 6 options and 9 options, rounded to two decimal places. A. B. C. D. E.

4.38 3.28 6.58 9.84 29.73 9

25.

Given the table below, what is the MAD and the MSE? Period 1 2 3 4

Actual 95 108 123 130

Forecast 100 110 120 130

MAD = ___________________

26.

The Acme Computer Company has recorded sales of one of its products for a six-week period: Using the three-week simple moving-average method, forecast sales for week 7. A. B. C. D. F.

27.

MSE = ___________________________

20 21 22 23 24

Week 1 2 3 4 5 6

Sales 25 23 20 22 23 24

The following table contains the number of consumer complaints received in a Publix supermarket in Florida. Use exponential smoothing with a constant of α = 0.33 to forecast the number of complaints in March, round to the nearest whole number of complaints. A. B. C. D. E.

39 42 45 53 64

Month January February March April May June

Number of Complaints 36 45 81 90 108 144

10

For the next 3 questions, consider the following summary output from Microsoft Excel for a simple regression of Halliburton (ticker symbol HAL) weekly stock prices on the S&P500 stock index, for the period January 2004 through August 2006.

SUMMARY OUTPUT Regression Statistics Multiple R 0.93 R Square 0.87 Adjusted R 0.86 Standard Error 3.20 Observations 140 ANOVA MS 9067.8 10.24

F 884.90

Significanc 6.84E-62

Standard 4.914

t Stat -24.74

Lower 95% -131.37

Upper -111.93

0.004

29.75

P-value 1.37E6.84E-

0.11

0.13

Regression Residual

Df 1 138

SS 9067.88 1414.13

Total

139

10482.0

Intercept

Coefficient -121.65

S&P500 Index

0.122

28.

According to the regression model, the correlation between Halliburton’s stock price and the S&P500 index value is: A. B. C. D. E.

29.

Positive. Negative. Significant and either positive or negative. Significant, but it cannot be determined whether the correlation is positive or negative. Not significant.

The regression model ABOVE is: A.

Not significant, because the standard error of the intercept is high compared to the standard error of the independent variable.

B.

Significant at the 0.01 level, because the coefficient of determination is less than 0.05.

C.

Significant at the 0.05 level, because the p-value is less than 0.05.

D.

Not significant, because the coefficient of determination is larger than 1.0.

E.

Significant at the 0.01 level, because the t-statistic is negative. 11

30.

According to the regression model ABOVE, when the S&P 500 index value is 1,000, the forecasted Halliburton stock price is: A. $29.75/share. B. $0.35/share. C. $122/share. D. $121.65/share. E. Cannot be determined from the tabulated data.

31.

Corporate AAA bond interest rates for 12 consecutive months are 9.5%, 9.3%, 9.4%, 9.6%, 9.8%, 9.7%, 9.8%, 10.5%, 9.9%, 9.7%, 9.6% and 9.6%. The three-month weighted moving average forecast (with weights 0.2, 0.4 and 0.4 - from oldest to most recent respectively) for the next month, rounded to two decimal places, is: A. 9.60% B. 9.65% C. 9.70% D. 9.62% E. None of the above.

Linear Programming The next two questions apply to this information: Quill Manufacturing Business makes two models of marking pens. An unlabeled graph for this problem and the requirements for each lot of pens in the three manufacturing departments are given below. All three departments are necessary in the production of both types of pens. The profit for either kind of pen is $1000 per lot. The dotted line represents the objective function line. Fliptop Model 3 5 5

Ink Assembly Molding Time Plastic

Tiptop Model 4 4 2

15

10

5

0 0

5

10

15

12

Available production hours 36 40 30

32.

What is the optimal production quantity of the Fliptop model? A. B. C. D. E.

33.

If all constraint inequalities in the original problem were ≥, then the following is true: A. B. C. D. E.

34.

The value of the objective function at the optimum solution is zero There will be multiple optimal solutions The problem will become unbounded The problem has a unique solution None of the above is true

Let M be the number of units to make and B be the number of units to buy of a certain product. If it costs $2 to make a unit and $3 to buy a unit and 4000 units are needed, the objective function of the LP model to minimize the cost of production would be: A. B. C. D. E.

35.

5 lots 4 lots 2 lots 7 lots 6 lots

Min 4000 (M + B) Max 8000M + 12000B Min 2M + 3B Max 2M + 3B Min 4000U -2M-3B

The Quiet Meadow Studio frames and sells photographs and prints. It cost $20 to purchase each photograph and it takes 2 hours to frame it. It costs $25 to purchase each print and it takes 5 hours to frame it. The store has at most $400 to spend and at most 60 hours to frame. The studio makes a $30 profit on each photograph and a $50 profit on each print. Determine the maximum profit. A. B. C. D. E.

360 600 700 740 800

13

The next two questions apply to this information: Quality Bike Maps has produced four map designs for the local area. A limited amount of time (in minutes) is allocated to the printing, cutting and folding of each map. Additionally, at least one thousand of map designs A, B, and C must be printed. The profit per map is $1 for A and B and $2 for C and D. The Excel output is provided below. Max Profit = A + B + 2 C + 2 D s.t. A + 2 B + 3 C + 3 D < 15000 2 A + 4 B + C + 3 D < 20000 3 A + 2 B + 5 C + 3 D < 20000 A > 1000 B > 1000 C > 1000

Print Cut Fold Print A Print B Print C

Microsoft Excel 14.0 Sensitivity Report Objective Function Value $10,166.67 Variable Cells

Cell $B$18 $C$18 $D$18 $E$18

Name Map A Map B Map C Map D

Final Value 1500 1000 1000 2833.33

Reduced Cost

Objective Coefficient 0 0 0 0

Final Value 15000 16500 20000 1500 1000 1000

Shadow Price 0.5 0 0.1666 0 -0.3333 -0.3333

1 1 2 2

Allowable Increase 1 0.3333 0.3333 1

Allowable Decrease 0.3333 1E+30 1E+30 0.5

Constraint R.H. Side 15000 20000 20000 1000 1000 1000

Allowable Increase 1000 1E+30 7000 500 1750 500

Allowable Decrease 5666.6666 3500 1000 1E+30 1000 1000

Constraints Cell $B$24 $B$25 $B$26 $B$27 $B$28 $B$29 36.

Name Print Cut Fold Print A Print B Print C

Answer the following question using the Excel output above. Which constraint(s) are binding? A. B. C. D. E.

Print and Fold Cut and Print A Print B and Print C Print and Cut Print, Fold, Print B and Print C

14

37.

Answer the following question using the Excel output above. Keeping within the confines of the problem, the profit on Map A has increased by one dollar. Determine the new objective function value. A. B. C. D. E.

38.

1,500 11,166.67 11,500.67 11,666.67 12,566.67

Quentin Magic Brown manufactures sports shoes and wants to maximize the company's profits. The company makes two types of sport shoe, Airwalkers and Bouncy Basketball shoes. The company earns $10 profit on each pair of Airwalkers and $18 profit on each pair of Bouncy Basketball shoes. The manufacturing process includes cutting the materials on a machine and having workers assemble the pieces. Each pair of Airwalkers requires 3 minutes of cutting time and the Bouncy Basketball shoes require 2 minutes. The machines that cut the material can run at most 1200 minutes a week. Each worker takes 7 hours to assemble a pair of Airwalkers and 8 hours to assemble a pair of Bouncy Basketball shoes; the maximum number of hours available is 3500 per week. Determine the maximum profit for this problem. A. B. C. D. E.

$3200 $4000 $4280 $6295 $7875

The next five questions apply to the Excel output for the Quantum Mo-Botics model is below. The company makes three types of machines and has limitations with regards to the amount of skilled and unskilled labor hours available and time on the assembly line. MAX Profit = 800SemiAuto+1000Robotic + 500Manual s.t. 30SemiAuto + 100Robotic + 45Manual < 4500 Skilled Labor 100SemiAuto + 70Robotic + 90Manual < 9000 Unskilled Labor 15SemiAuto + 20Robotic + 10Manual < 2000 Assembly Line Microsoft Excel 14.0 Sensitivity Report $ 82,025.32 Objective Function Value

15

Variable Cells Cell $B$18 $C$18 $D$18

Name SemiAuto Robotic Manual

Final Value 74.0506 22.7848 0

Reduced Cost

Objective Coefficient 0 800 0 1000 -320.2531 500

Allowable Increase 628.571 1666.666 320.253

Allowable Decrease 432.4786 440 1E+30

Name Skilled labor Unskilled labor Assembly line

Final Value 4500.00 9000.00 1566.456

Shadow Price 5.5696 6.3291 0

Allowable Increase 3605.263 3805.556 1E+30

Allowable Decrease 1800 5850 433.5443

Constraints Cell $B$24 $B$25 $B$26 39.

Answer the following question using the Excel output above. Determine the new objective function value if the profit on the second variable, Robotic, increases by $1000? A. B. C. D. E.

40.

$22,785.00 $19,125.64 $33,800.00 $102,805.32 $104,810.12

Answer the following question using the Excel output above. Keeping within the confines of the problem, how many more hours could you add to the skilled labor department? A. B. C. D. E.

41.

Constraint R.H. Side 4500 9000 2000

2875.33 1280.56 1550.56 3805.56 3605.26

Using the Excel output above, how much is each additional unit of unskilled labor worth? A. B. C. D. E.

$74.500 $22.790 $5.570 $6.329 $3.250

16

42.

Answer the following question using the Excel output above. Keeping within the confines of the problem, you are required to hire a full time (40 hours) person who is qualified to work in any department. Select the constraint where you will gain the most profit from this worker and determine the additiona...