Frandec Company manufactures, assembles, and rebuilds material hand equipment used in warehouses and distribution centers. One product, called a Liftmaster is assembled from four components: a frame, a motor, two supports, and a metal strap. Frandec is planning a production of 5000 Liftmasters next month. Frandec purchases the motors from an outside supplier, but the frames, supports, and straps may either be manufactured by the company or purchased from an outside supplier.
Manufacturing and purchase costs per unit are shown.

Component Manufacturing Costs Purchase cost
Frame $38.00 $51.00
Support 11.50 15.00
Strap 6.50 7.50

Three departments are involved in the production of these components. The time (in min per unit) required to process each component in each department is given, along with available capacity (in hours) for the three departments.

Component Cutting Dept Milling Dept Shaping Dept
Frame 3.5 2.2 3.1
Support 1.3 1.7 2.6
Strap 0.8 - 1.7
Capacity 350 420 680

a. Formulate and solve a linear programming model for this make-or-buy application. How many of each component should be manufactured and how many should be purchased?
b. What is the total cost of the manufacturing and purchasing plan?
c. How many hours of production time are used in each department?
d. How much should Frandec be willing to pay for an additional hour of time in the shaping department?