CLICK FOR ANSWERS MAT 540 Quantitative Methods Final Exam 2013 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). 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. What is the constraint on money to invest? 14. Given the following linear programming problem that minimizes cost. Min Z = 2x + 8y Subject to 8x + 4y ≥ 64 2x + 4y ≥ 32 y≥2 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: The Answer Report: The Sensitivity Report: 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. 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. 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. 18. 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? (Round your answer.) 23. Assume that it takes a college student an average of 5 minutes to find a parking spot in the main parking lot. Assume also that this time is normally distributed with a standard deviation of 2 minutes. What percentage of the 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. They know that at least 100 people will attend. The rental fee for the hall is $200 and the winning band will receive $500. In order to guarantee that they break even, how much should they charge for each ticket? (Note: Write your answer with two significant places after the decimal and do not include the dollar “$” sign. For instance, for five dollars, write your answer as 5.00). 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? (Note: The answer is a whole number. Give the answer as a whole number, omitting the decimal point. For instance, use 12 for twelve rooms). 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? (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). 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 $5. Total profit will increase by __________. Write your answers with two significant places after the decimal and do not include the dollar “$” sign. 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 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: 34. Find the optimal Z value for the following problem. Do not include the dollar “$” sign with your answer. Max Z = x1 + 6x2 Subject to: 17x1 + 8x2 ≤ 136 3x1 + 4x2 ≤ 36 x1, x2 ≥ 0 and integer 35. Let’s say that a life insurance company wants to update its actuarial tables. Assume that the probability distribution of the lifetimes of the participants is approximately a normal distribution with a mean of 72 years and a standard deviation of 5 years. What proportion of the plan participants are expected to survive to see their 75th birthday? Note: Round your answer, if necessary, to two places after the decimal. Please express your answer with two places after the decimal. 36. Ms. Hegel is considering four different opportunities, A, B, C, or D. The payoff for each opportunity will depend on the economic conditions, represented in the payoff table below. Investment Economic Conditions Poor (S1) Average (S2) Good (S3) Excellent (S4) A 80 15 18 47 B 50 75 35 35 C -90 225 -50 12 D 36 25 25 27 Suppose all states of the world are equally likely (each state has a probability of 0.25). What is the expected value of perfect information? Note: Report your answer as an integer, rounding to the nearest integer, if applicable 37. The local operations manager for the IRS must decide whether to hire 1, 2, or 3 temporary workers. He estimates that net revenues will vary with how well taxpayers comply with the new tax code. The probabilities of low, medium, and high compliance are 0.20, 0.30, and 0.50 respectively. What is the expected value of perfect information? Do not include the dollar “$” 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. Recent past demand for product ABC is given in the following table. Month Actual Demand May 33 June 32 July 39 August 37 The forecasted demand for May, June, July and August were 25, 30, 33, and 38 respectively. Determine the value of MAD. Note: Please express the result as a number with 2 decimal places. If necessary, round your result accordingly. For instance, 9.146, should be expressed as 9.15 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 â€œ$â€? sign with your answer.

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