Problem 1-09 (Algorithmic) Suppose the following is the mathematical model: wher

Question

Problem 1-09 (Algorithmic)

Suppose the following is the mathematical model:

where a is the number of hours required for each unit produced.

If we have a stochastic model in which the value of a varies between 2 and 5 (i.e., a = 2, a = 3, a = 4, or a = 5) as the possible values for the number of hours required per unit, what is the optimal value for x? If required, round your answer to two decimal places.

x =

What problems does this stochastic model cause?

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Explanation / Answer

We need to maximize 12x

s.to

ax <= 45 and x > 0

So,

for a = 2, x <= 45 / 2

X < = 22.5

optimal value of x = 22 hours (if decimal and fractional hours are not allowed)

for a = 3, x <= 45 / 3

X < = 15

optimal value of x = 15 hours

for a = 4, x <= 45 / 4

X < = 11.25

optimal value of x = 11 hours

for a = 5, x <= 45 / 5

X < = 9

optimal value of x = 9 hours

Hope this helps.

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