In an unbalanced transportation model, supply does not equal demand and one set of constraints uses ≤ signs.
Answer True False
Validation of a simulation model occurs when the true steady state average results have been reached.
Answer True False
Excel can be used to simulate systems that can be represented by both discrete and continuous random variables.
Answer True False
In a total integer model, all decision variables have integer solution values.
Answer True False
Fractional relationships between variables are not permitted in the standard form of a linear program.
Answer True False
If we are solving a 0-1 integer programming problem, the constraint x1 = x2 is a conditional constraint.
Answer True False
In a break-even model, if all of the costs are held constant, how does an increase in price affect the model? Answer
Breakeven point decreases
Breakeven point increases
Breakeven point does not change
The revenue per unit goes down
An equation or inequality that expresses a resource restriction in a mathematical model is called _____________________. Answer
a decision variable.
an objective function.
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: Answer
Events that cannot occur at the same time in any trial of an experiment are: Answer
In linear programming problems, multiple optimal solutions occur Answer
when constraint lines are parallel to each other.
when the objective function is parallel to a constraint line
every possible solution point violates at least one constraint
when the dual price for a particular resource is very small
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
B = 225, M = 0
B = 0, M = 225
B = 150, M = 75
B = 75, M = 150 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? Answer
Max Z = 75B + 85M
100B + 50M ≥ 25000
100B + 80M ≤ 18000
100B + 80M = 18000 5 points
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? Answer
0 to 4
2 to 5.33
0 to 5.33
4 to 6.33
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
paint and seal
Cannot tell from the information provided
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. An appropriate part of the model would be Answer
15X1 + 47.25X2 +110 X3 ≤ 50,000
MAX Z =15X1 + 47.25X2 + 110X3
X1 + X2 +X3 ≤ 50,000
MAX Z = 50(15)X1 + 50 (47.25)X2 + 50 (110)X3
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? Answer
X1 ≤ 0.35
X1 = 0.35 (50000)
X1 ≤ 0.35(X1 + X2 + X3)
X1 = 0.35(X1 + X2 + X3)
If we are solving a 0-1 integer programming problem, the constraint x1 = x2 is a __________ constraint. Answer
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 the constraint that indicates they have to use at least three of the five machines in their production. Answer
Y1 + Y2 + Y3 + Y4 + Y5 ≤ 3
Y1 + Y2 + Y3 + Y4 + Y5 = 3
Y1 + Y2 + Y3 + Y4 + Y5 ≥ 3
none of the above
The assignment problem constraint x31+x32+x33+x34 ≤ 2 means Answer
agent 3 can be assigned to 2 tasks
agent 3 can be assigned to no more than 2 tasks
a mixture of agents 1, 2, 3 and 4 will be assigned to tasks
agent 2 can be assigned to 3 tasks
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? Answer
XA1 +XA2 + XA3 + XA4 = 0
XA1 +XA2 + XA3 + XA4 = 1
XA1 +XA2 + XA3 + XA4 ≥ 1
XA1 +XA2 + XA3 + XA4 ≥ 0 5 points
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: Answer
controlled by the central limit theorem
all of the above
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? Answer
In the Monte Carlo process, values for a random variable are generated by __________ a probability distribution. Answer
A bakery is considering hiring another clerk to better serve customers. To help with this decision, records were kept to determine how many customers arrived in 10-minute intervals. Based on 100 ten-minute intervals, the following probability distribution and random number assignments developed.
Number of Arrivals
.01 – .10
.11 – .40
.41 – .70
.71 – .90
.91 – .00
Suppose the next three random numbers were .18, .89 and .67. How many customers would have arrived during this 30-minute period? Answer
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? Answer
For the following frequency distribution of demand, the random number 0.8177 would be interpreted as a demand of:
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.
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).
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).
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.
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)
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.
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, $9.45 (nine dollars and fortyfive cents) should be written as 9.45
Find the optimal Z value for the following problem. Do not include the dollar “$” sign with your answer.
Max Z = x1 + 6×2 Subject to: 17×1 + 8×2 ≤ 136 3×1 + 4×2 ≤ 36 x1, x2 ≥ 0 and integer
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.
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
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 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 = $50,000). Round to the nearest whole number, if necessary.
The following sales data are available for 2003-2008 :
Calculate the MAPD and express it in decimal notation. Please express the result as a number with 4 decimal places. If necessary, round your result accordingly. For instance, 9.14677, should be expressed as 9.1468
Consider the following decision tree. The objective is to choose the best decision among the two available decisions A and B. Find the expected value of the best decision. Do not include the dollar “$” sign with your answer.