• Question 1
Fractional relationships between variables are not permitted in the standard form of a linear program.
• Question 2
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 3
In an unbalanced transportation model, supply does not equal demand and one set of constraints uses = signs.
• Question 4
In a transshipment problem, items may be transported from destination to destination and from source to source.
• Question 5
If we are solving a 0-1 integer programming problem, the constraint x1 = x2 is a conditional constraint.
• Question 6
Validation of a simulation model occurs when the true steady state average results have been reached.
• Question 7
In a break-even model, if all of the costs are held constant, how does an increase in price affect the model?
Breakeven point decreases
Breakeven point decreases
• Question 8
An equation or inequality that expresses a resource restriction in a mathematical model is called _____________________.
a constraint.
a constraint.
• Question 9
Using the maximin criterion to make a decision, you
Look at the worst payoff for each possible decision and select the decision with the largest worst payoff
Look at the worst payoff for each possible decision and select the decision with the largest worst payoff
• Question 10
The probability of observing x
successes in a fixed number of trials is a problem related to
the binomial distribution
the binomial distribution
• Question 11
In linear programming problems, multiple optimal solutions occur
when the objective function is parallel to a constraint line
when the objective function is parallel to a constraint line
• Question 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?
100B + 80M = 18000
100B + 80M = 18000
• Question 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 objective function?
Max Z = 85B + 75M
Max Z = 85B + 75M
• Question 14
The Sensitivity Report:
Which additional resources would you recommend to be increased?
kiln
kiln
• Question 15
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:
same product mix, different total profit
same product mix, different total profit
• Question 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.
x11 + x12 = 8000
x11 + x12 = 8000
• Question 17
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?
X1 = 0.35(X1 + X2 + X3)
X1 = 0.35(X1 + X2 + X3)
• Question 18
In a capital budgeting problem, if either project 1 or project 2 is selected, then project 5 cannot be selected. Which of the alternatives listed below correctly models this situation?
x1 + x5 = 1, x2 + x5 = 1
x1 + x5 = 1, x2 + x5 = 1
• Question 19
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.
Y1 + Y4 = 1
Y1 + Y4 = 1
• Question 20
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 demanded by Customer B is:
X1B + X2B + X3B = 350
X1B + X2B + X3B = 350
• Question 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:
X1A + X1B + X1C = 500
X1A + X1B + X1C = 500
• Question 22
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?
62.47%
62.47%
• Question 23
79
75
• Question 24
Consider the following graph of sales.
Which of the following characteristics is exhibited by the data?
Trend plus irregular
Trend plus irregular
• Question 25
For the following frequency distribution of demand, the random number 0.8177 would be interpreted as a demand of:
0
2
• Question 26
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 Probability Random numbers
6 .1 .01 - .10
7 .3 .11 - .40
8 .3 .41 - .70
9 .2 .71 - .90
10 .1 .91 - .00
Suppose the next three random numbers were .18, .89 and .67. How many customers would have arrived during this 30-minute period?
24
24
• Question 27
In the Monte Carlo process, values for a random variable are generated by __________ a probability distribution.
sampling from
sampling from
• Question 28
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?
• Question 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
• Question 30
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?
• Question 31
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.
• Question 32
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.
• Question 33
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 $0.15 15 30
• Question 34
MAX Z = 5x1 + 8x2
s.t. x1 + x2 = 6
5x1 + 9x2 = 45
x1, x2 = 0 and integer
• Question 35
0.11
.10
.11
• Question 36
Mr. Sartre is considering four different opportunities, A, B, C, or D. The payoff for each opportunity will depend on the economic conditions, represented in the payoff table below.
Investment Economic Conditions
Poor
(S1) Average
(S2) Good
(S3) Excellent
(S4)
A 38 25 33 10
B 10 15 20 85
C 20 100 20 -25
D 25 25 100 25
• Question 37
The local operations manager for the IRS must decide whether to hire 1, 2, or 3 temporary workers. He estimates that net revenues will vary with how well taxpayers comply with the new tax code. The probabilities of low, medium, and high compliance are 0.20, 0.30, and 0.50 respectively. What is the expected value of perfect information? Do not include the dollar “$” sign with your answer. The following payoff table is given in thousands of dollars (e.g. 50 = $50,000).
• Question 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 = $50,000).
• Question 39
The following sales data are available for 2003-2008 :
Year Sales Forecast
2003 7 7
2004 8 8.5
2005 12 10.5
2006 14 13
2007 16 15
2008 18 16
Calculate the MAPD and express it in decimal notation. Please express the result as a number with 4 decimal places. If necessary, round your result accordingly. For instance, 9.14677, should be expressed as 9.1468
• Question 40
Consider the following decision tree. The objective is to choose the best decision among the two available decisions A and B. Find the expected value of the best decision. Do not include the dollar “$” sign with your answer.