We will revisit the milk production example discussed in class with more flexibility. Assume in this example we have again two products and two processes, however, we have the flexibility of using the machines interchangeably for processing the two products. Both products must go through both processes to finalize. Machine 1 Product 1 Product 2 Process 1 3 minutes/liter 2 minutes/liter Process 2 1 minutes/liter 2 minutes/liter Machine 2 Product 1 Product 2 Process 1 2 minutes/liter 3 minutes/liter Process 2 2 minutes/liter 1 minutes/liter Machine usage times per day: 12 hours for M1 and 6 hours for M2 Selling prices: Product 1 2.5$ per liter and Product 2 1.5$ per liter. You need to maximize daily total revenue. Decide if each of the following LP models is correct or not and discuss as to why! Model 1 Decision Variables: Xij: Amount of liters of product type i = 1, 2 that are processed in machine j = 1, 2 daily maximize 2.5(x11 + X12) + 1.5(x21 +222) s.t. 4x11 + 4221 0 i = 1, 2 j = 1, 2 Model 2 Decision Variables: Xijk : Amount in liters of product i going through process j in machine k max 2.5(2111 +2112) + 1.5(2221 +2222) s.t. 3x111 + X121 + 2x211 + 2x221 0 Model 3 Decision Variables: Xijk : Amount in liters of product i going through process j in machine k max 2.5(x111 + X112) + 1.5(x221 + x222) s.t. 3.x111 + x121 + 2x211 + 2.2221 0 Model 4 Decision Variables: Vijk : Amount in liters of product i going through process j in machine k max 2.5(x111 + X112) + 1.5(x221 + x222) s.t. 3x111 + X121 + 2x211 + 2x221 X121 + X 122 X211 + X212 > X221 + X222 X 111, X121, X211, 2221, X112, X122, X212,2222 > 0 Model 5 Decision Variables: Xijk: Amount of minutes product type i (i = 1, 2) spends in process j (j = 1, 2) on machine k (k = 1,2) max :) +1.5(+221 +2222) s.t. X 122 X 2.5(x121 + 2 X 121 + X111 + X211 + X221 + I 121 3 2 2 X211 X212 X 221 + > 2 3 2 X121, X111, X221, X211, X122, X112, X 222, X212 > 0 + X222