Please see attachment.

Problem 1

A variety of routine maintenance checks are made on commercial airplanes

prior to each takeoff. A particular maintenance check of an

airplaneâs landing gear requires between 10 and 18 minutes of a

maintenance engineerâs time. In fact, the exact time required is

uniformly distributed over this interval. As part of a larger

simulation model designed to determine total on-ground maintenance time

for an airplane, we will need to simulate the actual time required to

perform this maintenance check on the airplaneâs landing gear. Using

random numbers of 0.1567, 0.9823, 0.3419, 0.5572 and 0.7758, compute the

time required for each of five simulated maintenance checks of the

airplaneâs landing gear.

Problem 2

The management of Brinkley Corporation is interested in using simulation

to estimate the profit per unit for a new product. Probability

distributions for the purchase cost, the labor cost and the

transportation cost are as follows:

Purchase Cost ($) Probability Labor Cost ($) Probability Transportation

Cost ($) Probability

10 0.25 20 0.10 3 0.75

11 0.45 22 0.25 5 0.25

12 0.30 24 0.35 Â Â

Â Â 25 0.30 Â Â

Assume that these are the only costs and that the selling price for the

product will be $45 per unit.

Provide the base-case, worst-case and best case calculations for the

profit per unit.

Set up intervals of random numbers that can be used to randomly generate

the three cost components.

Using the random numbers 0.3726, 0.5839 and 0.8275, calculate the profit

per unit.

Using the random numbers 0.1862, 0.7466 and 0.6171, calculate the profit

per unit

Management believes the project may not be profitable if the profit per

unit is less than $5. Explain how simulation can be used to estimate

the probability the profit per unit will be less than $5.

Problem 3

Suppose that a decision maker faced with four decision alternatives and

four states of nature develops the following profit payoff table.

Â Â State of Nature Â

Decision Alternative S1 S2 S3 S4

d1 14 9 10 5

d2 11 10 8 7

d3 9 10 10 11

d6 8 10 11 13

If the decision maker knows nothing about the probabilities of the four

states of nature, what is the recommended decision using the optimistic,

conservative and minimax regret approaches?

Which approach do you prefer? Explain. Is establishing the most

appropriate approach before analyzing the problem important for the

decision maker? Explain.

Assume that the payoff table provides cost rather than profit payoffs.

What is the recommended decision using the optimistic, conservative and

minimax regret approaches?

Problem 1

A variety of routine maintenance checks are made on commercial airplanes

prior to each takeoff. A particular maintenance check of an

airplaneâs landing gear requires between 10 and 18 minutes of a

maintenance engineerâs time. In fact, the exact time required is

uniformly distributed over this interval. As part of a larger

simulation model designed to determine total on-ground maintenance time

for an airplane, we will need to simulate the actual time required to

perform this maintenance check on the airplaneâs landing gear. Using

random numbers of 0.1567, 0.9823, 0.3419, 0.5572 and 0.7758, compute the

time required for each of five simulated maintenance checks of the

airplaneâs landing gear.

Problem 2

The management of Brinkley Corporation is interested in using simulation

to estimate the profit per unit for a new product. Probability

distributions for the purchase cost, the labor cost and the

transportation cost are as follows:

Purchase Cost ($) Probability Labor Cost ($) Probability Transportation

Cost ($) Probability

10 0.25 20 0.10 3 0.75

11 0.45 22 0.25 5 0.25

12 0.30 24 0.35 Â Â

Â Â 25 0.30 Â Â

Assume that these are the only costs and that the selling price for the

product will be $45 per unit.

Provide the base-case, worst-case and best case calculations for the

profit per unit.

Set up intervals of random numbers that can be used to randomly generate

the three cost components.

Using the random numbers 0.3726, 0.5839 and 0.8275, calculate the profit

per unit.

Using the random numbers 0.1862, 0.7466 and 0.6171, calculate the profit

per unit

Management believes the project may not be profitable if the profit per

unit is less than $5. Explain how simulation can be used to estimate

the probability the profit per unit will be less than $5.

Problem 3

Suppose that a decision maker faced with four decision alternatives and

four states of nature develops the following profit payoff table.

Â Â State of Nature Â

Decision Alternative S1 S2 S3 S4

d1 14 9 10 5

d2 11 10 8 7

d3 9 10 10 11

d6 8 10 11 13

If the decision maker knows nothing about the probabilities of the four

states of nature, what is the recommended decision using the optimistic,

conservative and minimax regret approaches?

Which approach do you prefer? Explain. Is establishing the most

appropriate approach before analyzing the problem important for the

decision maker? Explain.

Assume that the payoff table provides cost rather than profit payoffs.

What is the recommended decision using the optimistic, conservative and

minimax regret approaches?

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