Question 5 (10 points): TechnoHearth produces heart valves that are made of the heart valves of pigs. There are three different sizes of pig valves that TechnoHearth buys from some suppliers (small size, medium size, and large size). In fact, TechnoHearth buys "batches\" of pig valves from 28 different suppliers. Table 1 provides information on the cost of a batch bought from different suppliers. This table also provides information on the number of valves with different sizes that a batch from each supplier includes. As an example, as Table 1 shows, one batch from Supplier 1 costs $3100 and includes 40 large valves, 10 medium valves, and 50 small valves. Similar information is available for other suppliers in Table 1. TechnoHearth must buy at least 300 large, 700 medium, and 500 small valves each week. Because of some operational reasons, TechnoHearth can buy at most 800 valves per week from each supplier. TAB L E 1 Supplier Cost Per hatch (S) The number of The number of The number of large valves in medium valves in small valves in each hatch each batch each hatch 1 3100 40 10 50 2 3000 54 78 64 3 4100 55 55 63 4 3500 18 73 76 5 2300 2? 85 10 6 5000 36 1? 23 7 2400 73 33 22 8 3100 45 88 13 9 3500 64 62 20 10 4500 7? 62 31 11 4300 35 42 38 12 3400 41 35 56 13 2300 74 51 31 14 2500 5? 32 65 15 3400 46 6? 85 16 5000 33 42 82 1? 2800 84 12 20 18 2200 49 39 55 19 3500 69 46 66 20 3700 33 10 38 21 4800 58 26 83 22 2700 45 66 5? 23 2400 70 8? 28 24 4600 15 59 6? 25 2700 54 45 18 26 2600 12 34 38 2? 4500 54 5? 7? 28 2600 28 42 82 4/7 Pa rt a) Formulate a mathematical programming model to minimize the total cost. (7 points) Pa rt b) How would you modify the model to ensure that at least 70 percent of purchased small valves are purchased from Supplier 3. (3 points)