Problem 1-09
Suppose the following is the mathematical model:
Max $10x$
s.t.
$ax \leq 40$
$x \geq 0$
where $a$ is the number of hours of production time required for each unit produced. With $a = 5$, the optimal solution is $x = 8$. If we have a stochastic model with $a = 3$, $a = 4$, $a = 5$, or $a = 6$ as the possible values for the
number of hours required per unit, what is the optimal value for $x$? Round your answers for the optimal solution to two decimal places. Round the answers for profit to the nearest dollar.
If $a = 3$, $x = $ 13.33 and profit = $ 133
If $a = 4$, $x = $ 10 and profit = $ 100
If $a = 5$, $x = $ 8 and profit = $ 80
If $a = 6$, $x = $ 6.67 and profit = $ 66
What problems does this stochastic model cause?
The problem with this stochastic model is $a$ is not known with certainty and therefore the values of $x$ and profit are not known with certainty.
