MAT540 – Final Exam

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.

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

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

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

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

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If we are solving a 0-1 integer programming problem, the constraintx1 =x2 is a conditional constraint.

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Using the maximin criterion to make a decision, you

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

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Using the minimax regret criterion to make a decision, you

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

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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:

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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?

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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 objective function?

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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?

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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?

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In a portfolio problem, X1, X2, and X3 represent the number of shares purchased of stocks 1, 2, an 3 which have selling prices of $15, $47.25, and $110, respectively. The investor has up to $50,000 to invest. The investor stipulates that stock 1 must not account for more than 35% of the number of shares purchased. Which constraint is correct?

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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.

The constraint for ingredient 3 is:

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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.

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If we are solving a 0-1 integer programming problem, the constraintx1 =x2 is a __________ constraint.

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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?

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A professor needs help from 3 student helpers to complete 4 tasks. The first task is grading; the second is scanning; the third is copying, and the fourth is organizing student portfolios. The estimated time for each student to do each task is given in the matrix below.

Which of the following constraints represents the assignment for student A?

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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.)

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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?

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

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In the Monte Carlo process, values for a random variable are generated by __________ a probability distribution.

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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?

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

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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).

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Carter’s Bed & Breakfast breaks even every month if they book 30 rooms over the course of a month. Their fixed cost is $1050 per month and the revenue they receive from each booked room is $150. What is the variable cost per occupied 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).

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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).

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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:

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.

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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 assembly? Write your answers with two significant places after the decimal and do not include the dollar “$” sign.

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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:

Kitty 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

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

MAX Z = 5×1 + 8×2

s.t. x1 + x2 ? 6

5×1 + 9×2 ? 45

x1, x2 ? 0 and integer

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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.

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Mr. Sartre 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.

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

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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

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.

The following sales data are available for 2003-2008 :

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 9.146

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.