Formulation Only. 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? Frandec Company manufactures, assembles, and rebuilds material$-$handling 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's production schedule calls for $5000$ Liftmasters to be made next month. Frandec purchases the motors from an outside supplier, but the frames, supports, and straps may be either manufactured by the company or purchased from an outside supplier. Manufacturing and purchase costs per unit are shown. Three departments are involved in the production of these components. The time $($in minutes per unit$)$ required to process each component in each department and the available capacity $($in hours$)$ for the three departments are as follows: