**MAT 540 Final Exam**

1). Fractional relationships between variables are not permitted in the standard form of a linear program.

2). In an unbalanced transportation model, supply does not equal demand and one set of constraints uses ≤ signs.

3). Excel can be used to simulate systems that can be represented by both discrete and continuous random variables.

4). In a transshipment problem, items may be transported from destination to destination and from source to source.

5). In a total integer model, all decision variables have integer solution values.

6). A cycle is an up and down movement in demand that repeats itself in less than 1 year.

7). Using the maximin criterion to make a decision, you

8). Using the minimax regret criterion to make a decision,

9). A business owner is trying to decide whether to buy, rent, or lease office space and has constructed the following payoff table based on whether business is brisk or slow. If the probability of brisk business is .40 and for slow business is .60, the expected value of perfect information is:

10). In a break-even model, if all of the costs are held constant, how does an increase in price affect the model?

11). Events that cannot occur at the same time in any trial of an experiment are:

12). Steinmetz furniture buys 2 products for resale: big shelves (B) and medium shelves (M). Each big shelf costs $100 and requires 100 cubic feet of storage space, and each medium shelf costs $50 and requires 80 cubic feet of storage space. The company has $25000 to invest in shelves this week, and the warehouse has 18000 cubic feet available for storage. Profit for each big shelf is $85 and for each medium shelf is $75. What is the storage space constraint?

13). Steinmetz furniture buys 2 products for resale: big shelves (B) and medium shelves (M). Each big shelf costs $100 and requires 100 cubic feet of storage space, and each medium shelf costs $50 and requires 80 cubic feet of storage space. The company has $25000 to invest in shelves this week, and the warehouse has 18000 cubic feet available for storage. Profit for each big shelf is $85 and for each medium shelf is $75. In order to maximize profit, how many big shelves (B) and how many medium shelves (M) should be purchased?

14). The following is an Excel “Answer” and “Sensitivity” reports of a linear programming problem: The Answer Report: The Sensitivity Report: Which additional resources would you recommend to be increased?

15). The production manager for Beer etc. produces 2 kinds of beer: light (L) and dark (D). Two resources used to produce beer are malt and wheat. He can obtain at most 4800 oz of malt per week and at most 3200 oz of wheat per week respectively. Each bottle of light beer requires 12 oz of malt and 4 oz of wheat, while a bottle of dark beer uses 8 oz of malt and 8 oz of wheat. Profits for light beer are $2 per bottle, and profits for dark beer are $1 per bottle. What is the optimal weekly profit?

16). The owner of Black Angus Ranch is trying to determine the correct mix of two types of beef feed, A and B which cost 50 cents and 75 cents per pound, respectively. Five essential ingredients are contained in the feed, shown in the table below. The table also shows the minimum daily requirements of each ingredient. Ingredient Percent per pound in Feed A Percent per pound in Feed B Minimum daily requirement (pounds) 1 20 24 30 2 30 10 50 3 0 30 20 4 24 15 60 5 10 20 40 The constraint for ingredient 3 is:

17). Let xij = gallons of component i used in gasoline j. Assume that we have two components and two types of gasoline. There are 8,000 gallons of component 1 available, and the demands for gasoline types 1 and 2 are 11,000 and 14,000 gallons respectively. Write the supply constraint for component 1.

18). The Kirschner Company has a contract to produce garden hoses for a customer. Kirschner has 5 different machines that can produce this kind of hose. Write a constraint to ensure that if machine 4 is used, machine 1 will not be used.

19). If we are solving a 0-1 integer programming problem, the constraint x1 = x2 is a __________ constraint.

20). The following table represents the cost to ship from Distribution Center 1, 2, or 3 to Customer A, B, or C. The constraint that represents the quantity supplied by DC 1 is:

21). The assignment problem constraint x31+x32+x33+x34 ≤ 2 means

22). Professor Dewey would like to assign grades such that 15% of students receive As. If the exam average is 62 with a standard deviation of 13, what grade should be the cutoff for an A? (Round your answer.)

23). Jack is considering pursuing an MS in Information Systems degree. He has applied to two different universities. The acceptance rate for applicants with similar qualifications is 30% for University X and 60% for University Y. The decisions of each university have no effect on each other. This means that they are:

24). __________ moving averages react more slowly to recent demand changes than do __________ moving averages.

25). Consider the following graph of sales. Which of the following characteristics is exhibited by the data?

26). For the following frequency distribution of demand, the random number 0.8177 would be interpreted as a demand of:

27). A bakery is considering hiring another clerk to better serve customers. To help with this decision, records were kept to determine how many customers arrived in 10-minute intervals. Based on 100 ten-minute intervals, the following probability distribution and random number assignments developed. Suppose the next three random numbers were .18, .89 and .67. How many customers would have arrived during this 30-minute period?

28). Ford’s Bed & Breakfast breaks even if they sell 50 rooms each month. They have a fixed cost of $6500 per month. The variable cost per room is $30. For this model to work, what must be the revenue per room? (Note: The answer is a whole dollar amount. Give the answer as a whole number, omitting the decimal point. For instance, use 105 to write $105.00).

29). Suppose that a production process requires a fixed cost of $50,000. The variable cost per unit is $10 and the revenue per unit is projected to be $50. Find the break-even point.

30). Joseph is considering pursuing an MS in Information Systems degree. He has applied to two different universities. The acceptance rate for applicants with similar qualifications is 30% for University X and 60% for University Y. What is the probability that Jim will not be accepted at either university? (Note: write your answer as a probability, with two decimal places. If necessary, round to two decimal places. For instance, a probability of 0.252 should be written as 0.25).

31). Consider the following linear program, which maximizes profit for two products, regular (R), and super (S): MAX 50R + 75S s.t. 1.2R + 1.6 S ≤ 600 assembly (hours) 0.8R + 0.5 S ≤ 300 paint (hours) .16R + 0.4 S ≤ 100 inspection (hours) Sensitivity Report:

Final Reduced Objective Allowable Allowable Cell Name Value Cost Coefficient Increase Decrease $B$7 Regular = 291.67 0.00 50 70 20 $C$7 Super = 133.33 0.00 75 50 43.75 Final Shadow Constraint Allowable Allowable

Cell Name Value Price R.H. Side Increase Decrease $E$3 Assembly (hr/unit) 563.33 0.00 600 1E+30 36.67 $E$4 Paint (hr/unit) 300.00 33.33 300 39.29 175 $E$5 Inspect (hr/unit) 100.00 145.83 100 12.94 40 A change in the market has increased the profit on the super product by $5. Total profit will increase by __________. Write your answers with two significant places after the decimal and do not include the dollar “$” sign.

32). Tracksaws, Inc. makes tractors and lawn mowers. The firm makes a profit of $30 on each tractor and $30 on each lawn mower, and they sell all they can produce. The time requirements in the machine shop, fabrication, and tractor assembly are given in the table. Formulation: Let x = number of tractors produced per period y = number of lawn mowers produced per period MAX 30x + 30y subject to 2 x + y ≤ 60 2 x + 3y ≤ 120 x ≤ 45 x, y ≥ 0 The graphical solution is shown below. What is the shadow price for fabrication? Write your answers with two significant places after the decimal and do not include the dollar “$” sign.

33). Klein Kennels provides overnight lodging for a variety of pets. An attractive feature is the quality of care the pets receive, including well balanced nutrition. The kennel’s cat food is made by mixing two types of cat food to obtain the “nutritionally balanced cat diet.” The data for the two cat foods are as follows:

Cat Food Cost/oz protien (%) fat (%) Partner’s Choice $0.20 45 20 Feline Excel $0.15 15 30 Klein Kennels wants to be sure that the cats receive at least 5 ounces of protein and at least 3 ounces of fat per day. What is the optimal cost of this plan? Note: Please write your answers with two significant places after the decimal and do not include the dollar “$” sign. For instance, $9.45 (nine dollars and fortyfive cents) should be written as 9.45

34). Find the optimal Z value for the following problem. Do not include the dollar “$” sign with your answer. Max Z = x1 + 6×2 Subject to: 17×1 + 8×2 ≤ 136 3×1 + 4×2 ≤ 36 x1, x2 ≥ 0 and integer

35). Suppose that x is normally distributed with a mean of 10 and a standard deviation of 3. Find P(x ≤ 6). Note: Round your answer, if necessary, to two places after the decimal. Please express your answer with two places after the decimal.

36). Ms. James is considering four different opportunities, A, B, C, or D. The payoff for each opportunity will depend on the economic conditions, represented in the payoff table below.

Investment Economic Conditions Poor (S1) Average (S2) Good (S3) Excellent (S4) A 18 25 50 80 B 19 100 50 75 C 100 26 120 60 D 20 27 50 240 Suppose all states of the world are equally likely (each state has a probability of 0.25). What is the expected value of perfect information? Note: Report your answer as an integer, rounding to the nearest integer, if applicable

37). The local operations manager for the IRS must decide whether to hire 1, 2, or 3 temporary workers. He estimates that net revenues will vary with how well taxpayers comply with the new tax code. The probabilities of low, medium, and high compliance are 0.20, 0.30, and 0.50 respectively. What is the expected value of perfect information? Do not include the dollar “$” sign with your answer. The following payoff table is given in thousands of dollars (e.g. 50 = $50,000). Note: Please express your answer as a whole number in thousands of dollars (e.g. 50 = $50,000). Round to the nearest whole number, if necessary.

38). The local operations manager for the IRS must decide whether to hire 1, 2, or 3 temporary workers. He estimates that net revenues will vary with how well taxpayers comply with the new tax code. The probabilities of low, medium, and high compliance are 0.20, 0.30, and 0.50 respectively. What are the expected net revenues for the number of workers he will decide to hire? The following payoff table is given in thousands of dollars (e.g. 50 = $50,000). Note: Please express your answer as a whole number in thousands of dollars (e.g. 50 = $50,000). Round to the nearest whole number, if necessary.

39). The following sales data are available for 2003-2008 :

Year Sales Forecast 2003 7 7 2004 8 8.5 2005 12 10.5 2006 14 13 2007 16 15 2008 18 16 Calculate the MAPD and express it in decimal notation. Please express the result as a number with 4 decimal places. If necessary, round your result accordingly. For instance, 9.14677, should be expressed as 9.1468

40). Consider the following decision tree. The objective is to choose the best decision among the two available decisions A and B. Find the expected value of the best decision. Do not include the dollar “$” sign with your answer.

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