The Magnetron Company manufactures and markets microwave ovens. Currently, the company produces two models: full-size and compact. Production is limited by the amount of labor available in the general assembly and electronic assembly departments, as well as by the demand for each model. Each full-size oven requires 2 hours of general assembly and 2 hours of electronic assembly, whereas each compact oven requires 1 hour of general assembly and 3 hours of electronic assembly. In the current production period, there are 500 hours of general assembly labor available and 800 hours of electronic assembly labor available.
In addition, the company estimates that it can sell at most 220 full-size ovens and 180 compact ovens in the current production period. The earnings contribution per oven is $120 for a full-size oven and $130 for a compact oven. The company would like to find an earnings-maximizing production plan for the current production period.
(a) Formulate the above problem as a linear optimization model.
(b) Solve the linear optimization model graphically. Plot the constraints, and identify each constraint and the feasible region. What is the optimal solution? Which constraints are binding at the optimal solution? What is the value of the objective function at the optimal solution?
(c) Consider the general assembly labor constraint. Suppose that the number 500 was changed to 510, i.e., the company has an additional 10 hours of general assembly labor. Re-solve the equations of the binding constraints to compute the new optimal solution. How does the new contribution to earnings differ from the contribution to earnings in part (b)? What is the marginal value of general assembly labor?