a) Compute the maximum number of Type A actuators that can be made and stay within the time constraints of all workstations. What is the profit? For completeness, do the same calculations if you only produce Type B actuators?

b)Now, use linear programming to find the solution that maximizes profit.For now, assume that we can produce fractions of actuators so the number to produce can be a continuous variable and we can use the methodology covered in the lessons.To find the number of Type A and Type B actuators that will maximize profit, perform the following step:

•Write the model in equation form.Let x A and x B be the number of actuators of type A and B to produce, respectively.Hint: You model will look something like problems 1 and 2. If z is the total profit the it will be equal to the profit gained from producing x A units of Type A plus the profit gained from producing x B units of Type B. There will be constraints for the each of the w/s’s that ensure the time used to produce x A and x Bis less than the total time available.

•Solve the model graphically for x*= (*Ax, *Bx)

•Compute the optimal profit (z*)that corresponds to x*.

•Compare this answer with your answers in part a) and note what you find. Which solution has the higher profit? What differences do you see in how the solutions utilize the w/s’s?