# Linear Programming MCQs Sample Assignment

Instructions

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Test 3 - Form A

Attempt 1

Question 1

Consider the following linear programming model: Max: X12 + X2 + 3X3  Subject to: X1 + X2 ≤ 3     X1 + X2 ≥ 1     X1, X2³ 0    This problem violates which of the following properties or assumptions?

1. certainty
2. proportionality
3. divisibility
4. linearity

Question 2

A redundant constraint is eliminated from a linear programming model.  What effect will this have on the optimal solution?

1. feasible region will decrease in size
2. feasible region will increase in size
3. a decrease in objective function value
4. no change

Question 3

Consider the following linear programming model:      Max X1 + X2      Subject to:      X1 + X2 ≤ 2      X1 ≥ 1      X2 ≥ 3      X1, X2 ≥ 0      This linear programming model has a(n)

1. alternate optimal solution
2. unbounded solution
3. redundant constraint
4. infeasible solution

Question 4

The constraint for a given resource is given by the following equation:  2X1 + 3X2 ≤ 20.  If X1 = 5 and X2 = 3, how many units of this resource are unused?

1. 20
2. 19
3. 1
4. 0

Question 5

In a product mix problem, a decision maker has limited availability of weekly labor hours.  Labor hours would most likely constitute a decision variable rather than a constraint.

1. True
2. False

Question 6

What is the constraint associated with job A for the following assignment problem?

 Machine Job 1 2 3 A \$3 \$4 \$2 B \$1 \$3 \$5 C \$6 \$4 \$2

Let Xij = 1 if job i is assigned to machine j, otherwise 0.

1. 3XA1 + 4XA2 + 2XA3 = 1
2. 3XA1 + 4XA2 + 2XA3 = -1
3. XA1 + XA2 + XA3 = -1
4. -XA1 - XA2 - XA3 = -1

Question 7

In an unbalanced transportation problem where total supply exceeds total demand, the supply constraints will typically have “≥” inequalities in keeping with our convention of writing flows out of nodes with negative constraint coefficients and expressing the supply at the node as a negative number.

1. True
2. False

Question 8

All supply and demand quantities in an assignment model equal one unit.

1. True
2. False

Question 9

In a maximal flow problem, the right hand-side of the flow balance constraints equals 1.

1. True
2. False

Question 10

It is possible to solve small assignment problems by enumerating all possible outcomes rather than modeling them as linear programming problems.

1. True
2. False

Question 11

Which of the following is not an approach to decision making under uncertainty?

1. maximax
2. maximin
3. Laplace
4. expected monetary value

Question 12

Determining the worst payoff for each alternative and choosing the alternative with the “best of the worst” is the approach called

1. maximax
2. maximin
3. Laplace
4. minimax regret

Question 13

The approach that is used for analyzing decision trees is called

1. maximax
2. maximin
3. Laplace
4. expected monetary value

Question 14

Consider the following payoff table that represents the profits earned for each alternative (A, B, and C) under the states of nature S1, S2, and S3.  Using the Laplace criterion, what would be the highest expected payoff?

 S1 S2 S3 A \$100 \$145 \$120 B \$75 \$125 \$110 C \$95 \$85 \$60
1. \$121.7
2. \$103.3
3. \$80
4. \$125

Question 15

The expected monetary value (EMV) represents a long term average payoff.

1. True
2. False

Question 16

Which of the following variables is considered random or probabilistic?

1. future interest rates
3. historical stock prices
4. historical interest rates

Question 17

The ABC Corporation is considering introducing a new product, which will require buying new equipment for a monthly payment of \$5,000.  Each unit produced can be sold for \$20.00.  ABC incurs a variable cost of \$10.00 per unit.  What is ABC’s monthly breakeven amount in dollars?

1. \$100,000.00
2. \$10,000.00
3. \$5,000.00
4. \$50,000.00

Question 18

If a decision model has one variable with a certain/deterministic input value and another variable with a random/probabilistic input, then the outcome of this model which is based on both variables will be probabilistic.

1. True
2. False

Question 19

A beauty saloon employs three hairdressers.  All customers get their hair washed in one area of the saloon before being taken to another area to get their hair cut.  Customer arrival rate and service time follows the Poisson and exponential distributions, respectively.  What is the Kendall notation for this system?

1. M/M/1
2. D/M/3
3. M/G/3
4. M/M/3

Question 20

A queuing system has an arrival rate of 5 customers per hour and a service rate of 8 customers per hour.  What is the utilization factor (ρ) of the system?

1. 40
2. 1.6
3. .625
4. 5

Question 21

Refer to the following information and output.

 Number of Servers 1.0 Arrival Rate 7.00 Service Rate 10.00 P(0), probability that there are no customers in the system 30% Lq, average length of the queue 1.63 W, average time in the system 0.33 L, average number of customers in the system 2.33 Wq, average time in the queue 0.23 Utilization factor of the system 70%

What is the probability that the service facility will be idle?

1. .23
2. .70
3. .33
4. .30

Question 22

Refer to the following information and output.

 Number of Servers 1.0 Arrival Rate 7.00 Service Rate 10.00 P(0), probability that there are no customers in the system 30% Lq, average length of the queue 1.63 W, average time in the system 0.33 L, average number of customers in the system 2.33 Wq, average time in the queue 0.23 Utilization factor of the system 70%

What is the average number of customers in the queue plus the number being served?

1. .70
2. 2.33
3. 1.63
4. .23

Question 23

What distribution is appropriate for simulating the event of rolling a single die?

1. continuous uniform
2. triangular
3. binomial
4. discrete uniform

Question 24

Simulation usually generates optimal solutions.

1. True
2. False

Question 25

The sum of the probabilities for all the experimental outcomes in a probability distribution must equal 1.

1. True
2. False