The Humber Transport Company has expanded its shipping capacity by purchasing 60 trailer trucks from a competitor that went bankrupt. The company subsequently iocated 20 of the purchased trucks at each of its shipping warehouses in Mississauga. Windsor, and Kingston. The company makes shipments from each of these warehouses to terminals in Montreal, New York, and Chicago. Each truck is capable of making one shipment per week. The terminal managers have each indicated their capacity for extra shipments. The manager at Montreal needs to accommodate 10 additional trucks per week, the manager at New York needs to accommodate 15 additional trucks per week, and the manager at Chicago needs to accommodate 25 additional trucks. The company makes the following profit per truckload shipment from each warehouse to each terminal. The profits differ as a result of differences in products shipped, shipping costs. and transport rates. Warehouse A B C Montreal New York Chicago m $2, 200 2:23 $2, 700 3:20 $3, 900 m $2, 400 2:33 32, 300 3:30 $4, 200 The company wants to know how many trucks to assign to each route (i.e.. warehouse to terminal) to maximize profit. In the table above 2,-3- represents the number of trucks assigned to route from warehouse 2' to terminal j. where 1 = Mississaugai = 2 = Windsor.i = 3 = Kingston A = Montreal,j = B = New York.j= C = Chicago Ci= Formulate a linear programming model for this problem. (a) The objective function for this problem is: O maximize Z = 3, 8003\" + 2, 200313 + 2, 400310 + 3, 10032,, + + 2, 700323 + 2, 800320 + 4, 600333 + 3, 900333 + 4, 200330 0 minimize Z = 3, 80031,; + 2, 200313 + 2, 400310 + 3, 10'3sz + + 2, 700323 + 2, 800320 + 4, 600233,! + 3, 900333 + 4, 2002330 0 maximize Z = 3, 800313 + 3, 100313 + 4, 600310 + 2, 200323 + + 2, 700323 + 3, 900320 + 2, 40033.4 + 2, 800333 + 4, 200330 0 minimize Z = 3, 80031,; -i- 3, 100313 + 4, 600310 + 2, 200323 + + 2, 700323 + 3, 900320 + 2, 400333 + 2, 800333 + 4, 20033c 0 None of the above. (b) Please choose the correct constraint: 031,4 + 313 + 313 2 20 031,, + 313 + 310 S 20 031,4 + 313 + 310 2 60 031,, + 323 + 330 2 20 031,, + 313 + 313 5 60 022124 + 3:23 + $30 $ 20 0 None of the above. (c) Please choose the correct constraint: 02:13 + 2:23 + 2:30 5 20 02:22! + 2:23 + 2:20 3 60 02:22; + 2:23 + 2:20 g 20 031A + 2:23 + 2:30 2 20 032A + 2:23 + 2:20 3_> 20 02:24 + 2:23 + 2:20 33 60 0 None of the above. (d) Please choose the correct constraint: 02:12; + 2:23 + 2:30 g 60 02:3,; + 2:33 + 2:30 g 20 031A + 2:23 + 2:30 3 20 02:33 + 2:33 + 2:30 2 20 02:32; + 2:33 + 2:30 2 60 02:13 + 2:23 + 9330 2 20 0 None of the above. (e) Please choose the correct constraint: 031A + 332.4 + $3,, 2 10 031A + 22% + 33,, 3_> 8, 400 031A + 32A + 33A 3 10 031A + 32A + 33,, = 10 031A + 32A + $3,; = 8, 400 031A + 32,4 + 33,, S 8, 400 0 None of the above. (1') Please choose the correct constraint in the standard form: 03:13 + 3:23 + $33 5 8, 600 03:13 + 323 + 3:33 5 15 03:13 + 3:23 + 3:33 2 15 02:13 + $23 + 333 l'_> 8, 600 03:13 + 3:23 + $33 = 15 0313 + 2:23 + $33 = 8, 600 0 None of the above. (9) Please choose the correct constraint in the standard form: 03:10 + 2:20 + 3:30 = 12, 700 03:10 + 2:20 + $30 5 25 03:10 + 2:20 + 330 S 12, 700 02:10 + 2:20 + 3:30 = 25 02:10 + $20 + 3:30 2 25 03:10 + 2:20 + 3:30 2 12, 700 0 None of the above. (h) Non-negativity for this LP problem means that: 03:13 + 2:23 + 2:33 2 0 031A X 3323 X 3330 33 0 02:10 + $20 + 9:30 2 0 031A + mm + 33A 2 0 Call 9:;3- > 0 O at least one 3.3 2 0 0 None of the above