Problem 4-17 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. Component Frame Support Strap Manufacturing Cost $38.00 $11.50 $6.50 Purchase Cost $51.00 $15.00 $7.50 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: Component Frame Support Strap Capacity (hours) Cutting 3.5 1.3 0.8 Department Milling 2.2 1.7 Shaping 3.1 2.6 1.7 680 350 420 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? 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 TP-number of straps purchased Min FM + FP + + SM + + SP + TM + s.t. FM + SM TM s FM 1 + + SM FM + SM + TM S FM + FP SM + + SP 2 TM + TP 2 FM, FP, SM, SP, TM, TP > 0 FM + SM TM s FM + FP 2 SM + SP T + TP 2 FM, FP, SM, SP, TM, TP 20 If required, round your answers to the nearest whole number. If an amount is zero, enter "o'. Manufacture Purchase Frames Supports Straps b. What the total cost of the manufacturing and purchasing plan? When required, round your answer to the nearest dollar. $ c. How many hours production time are used in each department? If required, round your answer to two decimal places. Hours of production Department time used Cutting hours Milling hours Shaping Inours d. How much should Frandec be willing to pay for an additional hour of time in the shaping department? If required, round your answers to the nearest whole number. If an amount is zero, enter 'o'. $ e. Another manufacturer has offered to sell frames to Frandec for $45 each. Could Frandec improve its position by pursuing this opportunity? Why or why not? If required, round your answers to the nearest cent. Because the current purchase price is $ The reduced cost is s which means that the solution may be improved if the cost is $ or below