7. A company has four manufacturing locations for a given product and six major markets. Each manufacturing center has different costs, and each market has different prices for the product. In addition the distances between manufacturing locations and markets varies and so does the transportation cost. The company has calculated the net profit, cj, of producing the good at location i and selling it in market j. These net profit figures, together with the maximum manufacturing capability at each location and demand at each market are shown in the table below. Markets Plants 1 2 3 1 29 44 63 51 2 51 43 37 53 3 59 29 63 54 4 54 63 62 51 5 56 53 46 43 6 27 46 47 38 1200 1800 1100 1900 1000 1200 700 1500 500 1100 (a) What is the optimal way for the company to produce and sell its product? [Hint: Remember that the company is a profit maximizer.] (b) What is the interpretation of the dual variables? (c) Which plant (if any) would you recommend expanding? (d) Which plant (if any) would you recommend reducing in size? (e) Which sales territory is the most profitable? (f) Which sales territory is the least profitable? PLEASE SOLVE IT IN GAMS AND INTERPRET THE RESULTS ACCORDING TO DUAL AND MARGINAL VALUES.