Question 1: (10 points) (This question can be solved in 20 minutes easily) We are to prepare an MPS for the future 3 periods. There are 2 different types of final products: Type A and Type B. Product Type Type A | Type B Forecasted demands DA = {200, 300, 500} units D3 = {180, 120, 200} units Unit variable production PA = 35$ PB = 85$ costs Unit inventory holding costs Unit backlogging costs ha = 4 S/period ba = 7 S/period ho= 8 $/period bp = 15 $/period There are two manufacturing departments at the plant: Cutting department and Assembly department. Operation time for Type A (man*hour/unit) 3.6 2.8 Operation time for Type B (man*hour/unit) 7.2 6.4 Production capacity (hour/period) 2500 3500 Cutting department Assembly department Fixed cost of making production in a period is 6000 $. We want to find the production amounts from each of the product types in each of the periods to satisfy the demands with the minimum total cost. Develop a Mixed Integer Programming (MIP) model for finding the optimal solution of the