Problem:

Suppose we modify the production model from Section 1.3 to obtain the following mathematical model: Max 10x s.t. ax 40 x > 0 where a is the number of hours required for each unit produced. With a= 5, the optimal solution is x=8. If we have a stochastic model in which the value of a varies between 3 and 6 (i.e., a= 3, a= 4, a= 5, or a= 6) as the possible values for the number of hours required per unit.

Required:

Question 1) What is the optimal value for x? What problems does this stochastic model cause? Solve the problem and show all work.