Question 6 (10 points): XYZ company produces metal shelves that are made of metal bars. There are three different sizes of metal bars that XYZ purchases from some suppliers (small-size bars, medium-size bars, large-size bar, extremely-large-size bar). In fact, XYZ buys "batches" of metal bars from 15 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 bars with different sizes that a batch from each supplier includes. As an example, as Table 1 shows, one batch from Supplier 1 costs $4400 and includes 16 extremely large bars, 28 large bars, 45 medium bars, and 37 small bars. Similar information is available for other suppliers in Table 1. XYZ must buy at least 600 extremely large, 540 large, 650 medium, and 790 small bars each week. Because of some operational reasons, XYZ can buy at most 1000 bars per week from each supplier. Table 1 Supplier Cost Per batch (S) The number of large bars in each batch The number of medium bar in each batch The number of small bars in each batch The number of extremely large bars in each batch 16 34 30 1 2 28 35 37 40 3 19 36 34 17 4 43 5 24 18 6 7 37 36 26 44 40 32 28 20 8 9 4400 3700 4400 3500 5300 4700 5100 5200 4700 3100 5600 4000 3300 3200 4100 4400 3500 5600 4200 4000 10 11 12 13 23 23 18 41 32 33 24 35 39 48 27 14 20 13 32 45 21 26 36 23 21 26 44 14 10 34 28 44 44 44 33 43 24 35 32 42 30 14 34 36 44 20 46 15 16 11 17 18 19 20 33 23 27 27 39 16 38 26 10 24 30 28 28 12 50 Part a) Formulate a mathematical programming model to minimize the total cost. (7 points) Part b) How would you modify the model to ensure that at least 60 percent of purchased small bars are purchased from Suppliers 4 and 5. (3 points) Question 6 (10 points): XYZ company produces metal shelves that are made of metal bars. There are three different sizes of metal bars that XYZ purchases from some suppliers (small-size bars, medium-size bars, large-size bar, extremely-large-size bar). In fact, XYZ buys "batches" of metal bars from 15 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 bars with different sizes that a batch from each supplier includes. As an example, as Table 1 shows, one batch from Supplier 1 costs $4400 and includes 16 extremely large bars, 28 large bars, 45 medium bars, and 37 small bars. Similar information is available for other suppliers in Table 1. XYZ must buy at least 600 extremely large, 540 large, 650 medium, and 790 small bars each week. Because of some operational reasons, XYZ can buy at most 1000 bars per week from each supplier. Table 1 Supplier Cost Per batch (S) The number of large bars in each batch The number of medium bar in each batch The number of small bars in each batch The number of extremely large bars in each batch 16 34 30 1 2 28 35 37 40 3 19 36 34 17 4 43 5 24 18 6 7 37 36 26 44 40 32 28 20 8 9 4400 3700 4400 3500 5300 4700 5100 5200 4700 3100 5600 4000 3300 3200 4100 4400 3500 5600 4200 4000 10 11 12 13 23 23 18 41 32 33 24 35 39 48 27 14 20 13 32 45 21 26 36 23 21 26 44 14 10 34 28 44 44 44 33 43 24 35 32 42 30 14 34 36 44 20 46 15 16 11 17 18 19 20 33 23 27 27 39 16 38 26 10 24 30 28 28 12 50 Part a) Formulate a mathematical programming model to minimize the total cost. (7 points) Part b) How would you modify the model to ensure that at least 60 percent of purchased small bars are purchased from Suppliers 4 and 5. (3 points)
