M3_A4. Midwest Electronics manufactures motors for small hand tools. The rnarlceting department is predicting sales of aaoo units in the next quarter. This is a new high and will test Midwest\"s productioi capacities. This motor is assembled from three components: a shaft, base, and cage. it is clear that some of these components will have to be purchased from outside suppliers due to [imited inhouse capacity. The variable in-house production cost per unit is compared with the outside cost in the table below: "NI-HOUSE PURCHASE COST FROM MR" UFACTUHEHG COST SUPPLIERS Shaft $1.513 3135 Base $3.35 $3.55 Cage $3.55 $4.00 Midwest's plant consists of three departments. The time requirements in hours for each component i: each department if manufactured in-house are summarized in the fo[lowing table. The hours available for production of this motor are listed in the last row. COMPONENT CUTTING DEPT. SHAPING DEPT. FRBRICATION DEPT. [hrsJunit] [hrsJunit] [hrsJunitl Shaft 0.04 CLUE CLUE Base CLUE DJ]? 0.0? Cage 01]? (1113 [1.03 Capacity.r {hrs.} BBB BBB BED Formulate and solve this problem in Excel to determine how manyr components should be produced andfor purchased to meet the requirements and minimize the cost. a} How manv decision variables does this problem have? b} Not counting the nonnegativity.r constraint how manv constraints does this problem have? c] What is the minimum cost in 1.iour optimal solution {the value ofthe objective function}? d} Based on vour solution how manv shafts shouid be made in-house? e] Based on vour solution how many shafts shouid be purchased from the supplier? f} Based on your solution how manv bases should be made inhouse? g} Based on 1,rour solution how manv bases should be purchased from the supplier? h} Based on vour solution how manv cages should be made in-house? i] Based on vour solution how many cag should be purchased from the supplier