# MAT 540 Final Exam 5

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**MAT 540 Final Exam**

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

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

3. Adjusted exponential smoothing is an exponential smoothing forecast adjusted for seasonality.

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

5. If we are solving a 0-1 integer programming problem, the constraint x1 = x2 is a conditional constraint.

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

7. 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. The conservative (maximin) strategy is:

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

9. The probability of observing x successes in a fixed number of trials is a problem related to

10. An equation or inequality that expresses a resource restriction in a mathematical model is called _____________________.

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

12. Steinmetz furniture buys 2 products for resale: big shelves (B) and medium shelves (M). ......What is the storage space constraint?

13. Steinmetz furniture buys 2 products for resale: big shelves (B) and medium shelves (M). ......Profit for each big shelf is $85 and for each medium shelf is $75. What is the constraint on money to invest?

14. Given the following linear programming problem that minimizes cost. What is the sensitivity range for the third constraint, y ≥ 2?

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

16. Let xij = gallons of component i used in gasoline j. Assume that we have two components and two types of gasoline. .........Write the supply constraint for component 1.

17. Compared to transportation LP problems, assignment problems are unique because

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. Consider the following network representation of shipment routes between plants, a distribution center, and retail outlets. The numbers next to the arcs represent shipping costs. For example, the cost of shipping from plant 1 to distribution center 3 is equal to 2.

21. 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:

22. Professor Truman would like to assign grades such that 10% 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?

23. Assume that it takes a college student an average of 5 minutes to find a parking spot in the main parking lot. ..........students will take between 2 and 6 minutes to find a parking spot in the main parking lot?

24. In the Monte Carlo process, values for a random variable are generated by __________ a probability distribution. 25. For the following frequency distribution of demand, the random number 0.8177 would be interpreted as a demand of:

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

27. __________ moving averages react more slowly to recent demand changes than do __________ moving averages. 28. Students are organizing a "Battle of the Bands" contest........

29. Nixon’s Bed and Breakfast has a fixed cost of $5000 per month and the revenue they receive from each booked room is $200. The variable cost per room is $75. How many rooms do they have to sell each month to break even?

30. 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?

31. Consider the following linear program, which maximizes profit for two products, regular (R), and super (S): A change in the market has increased the profit on the super product by $5. Total profit will increase by __________.

32. Consider the following linear program, which maximizes profit for two products, regular (R), and super (S): MAX

33. Kitty 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 data for the two cat foods are as follows:

34. Find the optimal Z value for the following problem. Do not include the dollar “$” sign with your answer.

35. Let’s say that a life insurance company wants to update its actuarial tables. .......What proportion of the plan participants are expected to survive to see their 75th birthday?

36. Ms. Hegel 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......

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. ..........

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 following payoff table is given in thousands of dollars (e.g. 50 = $50,000).

39. Recent past demand for product ABC is given in the following table. The forecasted demand for May, June, July and August were 25, 30, 33, and 38 respectively. Determine the value of MAD.

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

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