MAT540 Week 11 Final
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mat540_week_11_final.docxIn a transshipment problem, items may be transported from destination to destination and from source to source.
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True
False
Excel can be used to simulate systems that can be represented by both discrete and continuous random variables.
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True
False
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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Buy |
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Rent |
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Lease |
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Brisk. |
Events that cannot occur at the same time in any trial of an experiment are:
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exhaustive |
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dependent |
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independent |
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mutually exclusive |
In linear programming problems, multiple optimal solutions occur
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when constraint lines are parallel to each other. |
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when the objective function is parallel to a constraint line |
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every possible solution point violates at least one constraint |
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when the dual price for a particular resource is very small |
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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Breakeven point decreases |
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Breakeven point increases |
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Breakeven point does not change |
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The revenue per unit goes down |
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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Max Z = 75B + 85M |
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Max Z = 85B + 75M |
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100B + 50M ≤ 25000 |
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100B + 50M ≥ 25000 |
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100B + 80M ≤ 18000 |
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100B + 80M ≥ 18000 |
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?
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Max Z = 75B + 85M |
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100B + 50M ≥ 25000 |
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100B + 80M ≤ 18000 |
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100B + 80M = 18000 |
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?
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mix/mold |
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kiln |
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paint and seal |
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Cannot tell from the information provided |
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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XA1 +XA2 + XA3 + XA4 = 0 |
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XA1 +XA2 + XA3 + XA4 = 1 |
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XA1 +XA2 + XA3 + XA4 ≥ 1 |
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XA1 +XA2 + XA3 + XA4 ≥ 0 |
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:
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4X1A + 6X1B + 8X1C ≤ 500 |
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4X1A + 6X1B + 8X1C = 500 |
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X1A + X1B + X1C ≤ 500 |
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X1A + X1B + X1C ≥500 |
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:
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mutually exclusive |
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independent |
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controlled by the central limit theorem |
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all of the above |
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.
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0.03 |
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0.05 |
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0.07 |
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0.09 |
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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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).
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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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Kalamazoo 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:
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Cat Food |
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protien (%) |
fat (%) |
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Pet's Choice |
0.35 |
40 |
15 |
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Feline Chow |
0.32 |
20 |
30 |
Kalamazoo 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, $9.45 (nine dollars and fortyfive cents) should be written as 9.45
Find the optimal Z value for the following problem. Do not include the dollar “$” sign with your answer. MAX Z = 5x1 + 8x2 s.t. x1 + x2 ≤ 6 5x1 + 9x2 ≤ 45 x1, x2 ≥ 0 and integer
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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 68 years and a standard deviation of 4 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.
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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.
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Poor (S1) |
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Excellent (S4) |
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A |
80 |
15 |
18 |
47 |
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B |
50 |
75 |
35 |
35 |
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-90 |
225 |
-50 |
12 |
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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
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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 = $50,000). Round to the nearest whole number, if necessary.
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5 points
The local operations manager for the IRS must decide whether to hire 1, 2, or 3 temporary workers. He estimates that net revenues will vary with how well taxpayers comply with the new tax code. The probabilities of low, medium, and high compliance are 0.20, 0.30, and 0.50 respectively. What is the expected value of perfect information? Do not include the dollar “$” 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 = $50,000). Round to the nearest whole number, if necessary.
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Recent past demand for product DEF is given in the following table.
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19 |
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June |
20 |
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July |
23 |
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August |
21 |
The forecasted demand for May, June, July and August were 17, 18, 20 and 24 respectively. Determine the value of MAD. Note: Please express the result as a number with 2 decimal places. If necessary, round your result accordingly. For instance, 9.146, should be expressed as 9.15
Consider the following decision tree. The objective is to choose the best decision among the two available decisions A and B. Find the expected value of the best decision. Do not include the dollar “$” sign with your answer.
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