Statistics and probability question on linear programming equation

The Humber Transport Company has expanded its shipping capacity by purchasing 105 trailer trucks from a competitor that went bankrupt. The company subsequently located 35 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 in Montreal needs to accommodate 25 additional trucks per week, the manager in New York needs to accommodate 45 additional trucks per week, and the manager in Chicago needs to accommodate 30 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. Terminal Warehouse A B C Montreal New York Chicago 1. Mississauga CIA $4800 C1B $5200 C10 $5100 2. Windsor 2A $2600 X2B $2700 x20 $3900 3. Kingston C3A $3400 X3B $3900 30 $4800 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, @j represents the number of trucks assigned to the route from warehouse i to terminal j, where i 1 = Mississauga, i = 2 = Windsor, i = 3 = Kingston A = Montreal, j = B = New York, j = C = Chicago Formulate a linear programming model for this problem. (a) The objective function for this problem is: maximize Z = 4800x1A + 2600X1B + 3400x1C + 5200x24 + + 2700x2B + 3900x2c + 51003A + 3900x3B + 4800x30 minimize Z = 4800x1A + 2600X1B + 3400xic + 5200x24 + + 2700x2B + 3900x2C + 5100x3A + 3900x3B + 4800x30 minimize Z = 4800x1A + 5200X1B + 5100x1C + 2600x24 + + 2700x2B + 3900x2c + 3400x3A + 3900x3B + 4800x30 maximize Z = 4800x1A + 5200X1B + 5100x1C + 2600x24 + + 2700x2B + 3900x2c + 3400x3A + 39003B + 4800x30 None of the above.[b] Please 31A 131A m1A 31A 31A choose the correct constraint: $13 + 1310 S 35 .1313 + $10 2 105 11:13 + 2310 2 35 $23 + $30 2 35 :1':2B + 2330 S 35 31A None (c) Please m1A m1A m2A m2A 32A - $13 + 2310 S 105 of the above. choose the correct constraint: 2223 + 2230 S 35 - $23 + $30 2 35 - $23 + $20 5 35 - $23 + $20 2 35 2223 + .1320 2 105 32A None (d) Please 133A 133A 133A m1A 31A 2323 + 2320 5 105 of the above. choose the correct constraint: - $33 + $30 2 35 - $33 + $30 2 105 - $33 + $30 5 35 - $23 + 2330 S 105 423 + $30 2 35 31A None [e] Please 5131A 31A' 31A m1A mlA' $23+$3C S 35 of the above. choose the correct constraint: - $2A + 133A 5 25 32A + 33A S 10800 32A + 133A 2 10800 - 32A + 5133A 2 25 -$2A + 33A = 25 31A None '32A +'33A_Z 10300 of the above. (f) Please choose the correct constraint in the standard form: $13 $23 1333:45 3:13 .1323 2233:11800 31B 3323 2933311800 $13 2323 $33 2 11800 $1313 1323 2333345 31B 2323 2333245 None of the above. (9) Please choose the correct constraint in the standard form: 310 $20 2330230 x10 51320 $302 13800 310 $20 $36530 x10 1320 1330:30 $10 2320 2230213800 $10 .1820 1:305 13800 None of the above. (h) Non-negativity for this LP problem means that: all my 2 0 31A X 2323 X $30 2 0 at=10 + $20 + $30 2 0 331A + 32A + 333.4 2 0 at least one my 2 0 31H + 2323 +333 2 0 None of the above