1. The following linear programming problem has been written to plan the production of two products using two inputs - labor and materials. The company wants to maximize its profits, it can not produce more than 53 units of X1 X = number of product 1 produced in each batch X2 = number of product 2 produced in each batch MAX: 150 X1 + 250 X Subject to: 2X1 +5X2 s 200 (labor) 3 X, +7X2 5180 (materials) Xis 53 X1, X220 a) Draw the feasible region and solve the corner points manually and step by step. b) Solve the problem graphically. Find the optimal bundle of product 1 and 2. Show the optimal value of the objective function. c) What is the shadow price of materials, if we measure the shadow price of materials as the change of profit due to one unit change of available materials? Is it profitable to buy more materials form the market if the market price is $20? (Extra 0.5 points, due before Thursday) (Hint: you might want to change the RHS of Inaterials from 180 to 181 and then compare the optimal value of obj)