16. A firm supplies six outlets with two commodities, A and B, produced at three plants. The transportation costs vary from plant to market and are also dependent 56 CHAPTER 2. THE LINEAR PROGRAMMING MODEL on the commodity being shipped. Moreover, there are upper-bound capacities on the combined total number of units that can be shipped from each plant to each market. Determine if it is possible to meet the demands with the supplies given the restrictions on the shipping capacities and, if so, determine a minimal cost shipping schedule. The data are: Plant 2 1 3 Supplies Units of A Units of B 1000 1400 2500 1500 1500 1100 Outler 3 4 1 2 5 6 Demands Units of A Units of B 1200 800 600 800 1100 1000 1000 SOO 500 300 600 600 To Outlet 3 4 From Plant 1 2 S 6 Commodity A B 7 26 17 35 19 27 13 32 20 23 12 40 25 Shipping Costs (cents/unit) 2 A B 48 20 56 32 70 45 45 25 55 30 60 32 39 3 B 30 21 40 33 35 29 32 25 32 To Outlet 3 4 From Plant 1 2 5 6 Shipping Capacities 1 2 3 600 600 800 500 500 500 1000 2000 0 500 2000 2000 300 350 250 650 450 400 16. A firm supplies six outlets with two commodities, A and B, produced at three plants. The transportation costs vary from plant to market and are also dependent 56 CHAPTER 2. THE LINEAR PROGRAMMING MODEL on the commodity being shipped. Moreover, there are upper-bound capacities on the combined total number of units that can be shipped from each plant to each market. Determine if it is possible to meet the demands with the supplies given the restrictions on the shipping capacities and, if so, determine a minimal cost shipping schedule. The data are: Plant 2 1 3 Supplies Units of A Units of B 1000 1400 2500 1500 1500 1100 Outler 3 4 1 2 5 6 Demands Units of A Units of B 1200 800 600 800 1100 1000 1000 SOO 500 300 600 600 To Outlet 3 4 From Plant 1 2 S 6 Commodity A B 7 26 17 35 19 27 13 32 20 23 12 40 25 Shipping Costs (cents/unit) 2 A B 48 20 56 32 70 45 45 25 55 30 60 32 39 3 B 30 21 40 33 35 29 32 25 32 To Outlet 3 4 From Plant 1 2 5 6 Shipping Capacities 1 2 3 600 600 800 500 500 500 1000 2000 0 500 2000 2000 300 350 250 650 450 400