Problem #1 (30 points; 10 points each question) A trucking company is trying to haul sand from four warehouses to four construction sites according to the following schedule. Warehouse 1 Warehouse 2 Warehouse 3 Warehouse 4 3. Site A: 130 2 Site B: 100 1 3 1 2 Site C: 120 2 3 3 Site D: 138 2 2 1 To interpret the table, take the first row as an example. To ship sand from warehouse 1 to site A, each truck can take 3 tons. To ship sand from warehouse 2 to site A, each truck can take 2 tons... Site A will need 130 tons of sand in total. The other rows can be interpreted similarly. 1.1 1.2 Present the problem in a system of linear equations to find out how many trucks are needed at each warehouse so that the need of the four sites is met exactly. Solve the question system by rewriting it into the AX = B format and then use matrix method with computer to solve. Be sure to include all detailed steps and a conclusion. Write out or copy and paste the inverse matrix you will use. Suppose instead of the current numbers in the fourth row, the new numbers along the row are 2, 1, 2, 1 instead (site D remains 138 tons), try to use the same method as in 1.2 to solve the system. Comment on the inverse matrix. [This last part is a bonus question worth 5 additional points: given the new numbers in the fourth row, show how changing the last number in the fourth row (i.e., 138) may lead to different answers.] 1.3 Problem #1 (30 points; 10 points each question) A trucking company is trying to haul sand from four warehouses to four construction sites according to the following schedule. Warehouse 1 Warehouse 2 Warehouse 3 Warehouse 4 3. Site A: 130 2 Site B: 100 1 3 1 2 Site C: 120 2 3 3 Site D: 138 2 2 1 To interpret the table, take the first row as an example. To ship sand from warehouse 1 to site A, each truck can take 3 tons. To ship sand from warehouse 2 to site A, each truck can take 2 tons... Site A will need 130 tons of sand in total. The other rows can be interpreted similarly. 1.1 1.2 Present the problem in a system of linear equations to find out how many trucks are needed at each warehouse so that the need of the four sites is met exactly. Solve the question system by rewriting it into the AX = B format and then use matrix method with computer to solve. Be sure to include all detailed steps and a conclusion. Write out or copy and paste the inverse matrix you will use. Suppose instead of the current numbers in the fourth row, the new numbers along the row are 2, 1, 2, 1 instead (site D remains 138 tons), try to use the same method as in 1.2 to solve the system. Comment on the inverse matrix. [This last part is a bonus question worth 5 additional points: given the new numbers in the fourth row, show how changing the last number in the fourth row (i.e., 138) may lead to different answers.] 1.3
