# Mat 540 final exam 2015 data 200 out of 200

Validation of a simulation model occurs when the true steady state average results have been reached. • Question 2 5 out of 5 points Fractional relationships between variables are not permitted in the standard form of a linear program. • Question 3 5 out of 5 points In a 0-1 integer programming problem involving a capital budgeting application (where xj = 1, if project j is selected, xj = 0, otherwise) the constraint x1 – x2 ≤ 0 implies that if project 2 is selected, project 1 cannot be selected. • Question 4 5 out of 5 points In a transshipment problem, items may be transported from destination to destination and from source to source. • Question 5 0 out of 5 points Adjusted exponential smoothing is an exponential smoothing forecast adjusted for seasonality. Answer • Question 6 5 out of 5 points In an unbalanced transportation model, supply does not equal demand and one set of constraints uses ≤ signs. • Question 7 5 out of 5 points 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: A • Question 8 5 out of 5 points In a break-even model, if all of the costs are held constant, how does an increase in price affect the model? Answer • Question 9 5 out of 5 points Using the maximin criterion to make a decision, you Answer • Question 10 5 out of 5 points 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. • Question 11 5 out of 5 points Using the minimax regret criterion to make a decision, you Answer • Question 12 5 out of 5 points 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? Answer • Question 13 5 out of 5 points 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? • Question 14 0 out of 5 points For a maximization problem, assume that a constraint is binding. If the original amount of a resource is 4 lbs., and the range of feasibility (sensitivity range) for this constraint is from 3 lbs. to 6 lbs., increasing the amount of this resource by 1 lb. will result in the: Answer • Question 15 5 out of 5 points 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? Answer • Question 16 5 out of 5 points 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. • Question 17 5 out of 5 points 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: • Question 18 5 out of 5 points If we are solving a 0-1 integer programming problem, the constraint x1 = x2 is a __________ constraint. Answer • Question 19 5 out of 5 points 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. • Question 20 5 out of 5 points 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. Assume that Plant 1 can supply 400 units and Plant 2, 500 units. Demand at the retail outlets are: Outlet 4, 300 units; Outlet 5, 250 units; Outlet 6, 450 units. Supply is less than demand, so this is an unbalanced transshipment model. Which constraint represents the quantity shipped to retail outlet 6? • Question 21 5 out of 5 points 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: Answer • Question 22 5 out of 5 points The metropolitan airport commission is considering the establishment of limitations on noise pollution around a local airport. At the present time, the noise level per jet takeoff in one neighborhood near the airport is approximately normally distributed with a mean of 100 decibels and a standard deviation of 3 decibels. What is the probability that a randomly selected jet will generate a noise level of more than 105 decibels? Note: please provide your answer to 2 places past the decimal point, rounding as appropriate. • Question 23 5 out of 5 points 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.) • Question 24 5 out of 5 points Given an actual demand of 59, a previous forecast of 64, and an alpha of .3, what would the forecast for the next period be using simple exponential smoothing? • Question 25 5 out of 5 points __________ moving averages react more slowly to recent demand changes than do __________ moving averages. Answer • Question 26 5 out of 5 points For the following frequency distribution of demand, the random number 0.8177 would be interpreted as a demand of: • Question 27 5 out of 5 points In the Monte Carlo process, values for a random variable are generated by __________ a probability distribution. s • Question 28 5 out of 5 points 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). • Question 29 5 out of 5 points 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. • Question 30 5 out of 5 points 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). • Question 31 5 out of 5 points 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. • Question 32 0 out of 5 points 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. • Question 33 0 out of 5 points 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, $9.45 (nine dollars and fortyfive cents) should be written as 9.45 • Question 34 5 out of 5 points Find the optimal Z value for the following problem. Do not include the dollar “$” sign with your answer. MAX Z = 5x1 + 8x2 s.t. x1 + x2 ≤ 6 5x1 + 9x2 ≤ 45 x1, x2 ≥ 0 and integer Answer • Question 35 5 out of 5 points Let us take as a given that x is normally distributed with a mean of 8.5 and a standard deviation of 2, what is 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. • Question 36 5 out of 5 points 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 Answer • Question 37 5 out of 5 points 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 = $50,000). Round to the nearest whole number, if necessary. • Question 38 5 out of 5 points The local operations manager for the IRS must decide whether to hire 1, 2, or 3 temporary workers. He estimates that net revenues will vary with how well taxpayers comply with the new tax code. The probabilities of low, medium, and high compliance are 0.20, 0.30, and 0.50 respectively. What is the expected value of perfect information? Do not include the dollar “$” 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 = $50,000). Round to the nearest whole number, if necessary. • Question 39 5 out of 5 points The following sales data are available for 2003-2008 : Year Sales Forecast 2003 7 9 2004 12 10 2005 14 15 2006 20 22 2007 16 18 2008 25 21 Calculate the MAPD and express it in decimal notation. Please express the result as a number with 4 decimal places. If necessary, round your result accordingly. For instance, 9.14677, should be expressed as 9.1468 • Question 40 5 out of 5 points Consider the following decision tree. The objective is to choose the best decision among the two available decisions A and B. Find the expected value of the best decision. Do not include the dollar “$” sign with your answer.