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**Test 3 - Form A**

**Attempt 1**

**Question 1**

Consider the following linear programming model: Max: X_{1}^{2} + X_{2} + 3X_{3} Subject to: X_{1} + X_{2} ≤ 3 X_{1} + X_{2} ≥ 1 X_{1}, X_{2}³ 0 This problem violates which of the following properties or assumptions?

- certainty
- proportionality
- divisibility
**linearity**

**Question 2**

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

- feasible region will decrease in size
- feasible region will increase in size
- a decrease in objective function value
**no change**

**Question 3**

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

- alternate optimal solution
- unbounded solution
- redundant constraint
**infeasible solution**

**Question 4**

The constraint for a given resource is given by the following equation: 2X_{1} + 3X_{2} ≤ 20. If X_{1} = 5 and X_{2} = 3, how many units of this resource are unused?

- 20
- 19
**1**- 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.

- True
**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 X_{ij} = 1 if job i is assigned to machine j, otherwise 0.

- 3X
_{A1}+ 4X_{A2}+ 2X_{A3}= 1 - 3X
_{A1}+ 4X_{A2}+ 2X_{A3}= -1 - X
_{A1}+ X_{A2}+ X_{A3}= -1 **-X**_{A1}- X_{A2}- X_{A3}= -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.

- True
**False**

**Question 8**

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

**True**- False

**Question 9**

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

- True
**False**

**Question 10**

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

**True**- False

**Question 11**

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

- maximax
- maximin
- Laplace
**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

- maximax
**maximin**- Laplace
- minimax regret

**Question 13**

The approach that is used for analyzing decision trees is called

- maximax
- maximin
- Laplace
**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 |

**$121.7**- $103.3
- $80
- $125

**Question 15**

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

**True**- False

**Question 16**

Which of the following variables is considered random or probabilistic?

**future interest rates**- last year’s advertising budget
- historical stock prices
- 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?

- $100,000.00
**$10,000.00**- $5,000.00
- $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.

**True**- 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?

- M/M/1
- D/M/3
- M/G/3
**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?

- 40
- 1.6
**.625**- 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?

- .23
- .70
- .33
**.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?

- .70
**2.33**- 1.63
- .23

**Question 23**

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

- continuous uniform
- triangular
- binomial
**discrete uniform**

**Question 24**

Simulation usually generates *optimal* solutions.

- True
**False**

**Question 25**

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

**True**- False

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