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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 5,500 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. Component Manufacturing Cost Purchase Cost Frame $37.00 $50.00 Support $10.50 $14.00 Strap $5.50 $6.50 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. Department Component Cutting Milling Shaping Frame 3.5 2.2 3.1 Support 1.3 1.7 2.6 Strap 0.8 - 1.7 Capacity (hours) 350 420 680 (a) Formulate and solve a linear programming model for this make-or-buy application. (Let FM = number of frames manufactured, FP = number of frames purchased, SM = number of supports manufactured, SP = number of supports purchased, TM = number of straps manufactured, and TP = number of strap purchased. Express time in minutes per unit.) Min 37FM + 50FP + 10.5SM + 14SP + 5.57M + 6.57P Cutting constraint 21000 X Milling constraint 25200 X Shaping constraint 40800 X Frame constraint 5500 x Support constraint 11000 X Strap constraint 5500 X FM, FP, SM, SP, TM, TP 20 How many of each component should be manufactured and how many should be purchased? (Round your answers to the nearest whole number.) (FM, FP, SM, SP, TM, TP) = 388538