The Ace Manufacturing Company has orders for three similar products. Three machines are available for the manufacturing operations. All three machines can produce all the products at the same production rate. However, due to varying defect percentages of mch product on each machine, the unit costs of the products vary depending on the machine used. Machine capacities for the next week and the unit costs are shown below. Use the transportation model to develop the minimum cost production schedule for the products and machines. Use the transportation model to develop the minimum cost production schedule for the products and machines. (a) Show the linear programming formulation. (Let X, be the number of units of product A produced by machine 1, x;; be the number of units of product / produced by machine j, etc.) Min X41 + 1.30X 42 + 1.10x 43 + 1.20xB1 + 1.40xB2 + *$3 + 0.90xc1 + 1.20x(2 + 1.20%C3 s.t. Machine 1 Capacity *AIXBIXC1 1000 X Machine 2 Capacity * 42 + *B2 + * C2 5 1500 Machine 3 Capacity *43 + *B3 + * 03 900 Product A Orders *A1 *42 + X 43 = 1900 Product B Orders *B1 *B2 + *B3 = 500 Product C Orders *1 7 *02 + *03 = 1200 x;; 2 0 for all i, j. (b) Show the production schedule. (XA1( XAZI XABI XBI' XBZ XB3 XCI( XCZ' XC3) = 1500, 0, 500, 0, 0, 500, 0, 1200, 0 X (c) Determine the cost (in dollars) of the production schedule. Total = $ 3600 X