3.22.* A cargo plane has three compartments for storing cargo: front, center, and back. These compartments have capacity limits on both weight and space, as summarized below. Page 111 Compartment Weight Capacity (Tons) Space Capacity (Cubic Feet) Front 12 7,000 Center 18 9,000 Back 10 5,000 Furthermore, the weight of the cargo in the respective compartments must be the same proportion of that compartment's weight capacity to maintain the balance of the airplane. The following four cargoes have been offered for shipment on an upcoming flight as space is available. Cargo Weight (Tons) Volume (Cubic Feet/Ton) Profit ($/Ton) 1 20 500 320 2 16 700 400 3 25 600 360 4 13 400 290 Any portion of these cargoes can be accepted. The objective is to determine how much (if any) of each cargo should be accepted and how to distribute each among the compartments to maximize the total profit for the flight. Answer the following questions based on Problem 3.22 in the textbook (Page 111). This problem can be considered as a special case of the transportation problem with Cargo 1, 2, 3, 4, 5 on one side and Compartment Front, Center, and Back on the other side of the graph. As a result, the variables are defined as Xij where i=1,2,3,4 and j=F, C, B. For example, X2c denotes the tons of Cargo 2 to be placed in the Center compartment. (1) The objective function is : Max X1F + XC + X1B + X2F + X2C + X2B + X3F + + X3B + X4F + X4C + X4B For the following questions, enter the LHS of the constraint with the coefficient and variable name, for example, 235X1C. If the coefficient is "", just enter the variable name, for example, X1C instead of 1X1C. Then choose the direction of the constraint, =". Finally, enter the RHS constant. (2) Write the compartment weight capacity constraint for the Center compartment. (Please follow the order these variables appeared the objective function.) (Click to select) v + + (3) Write the resource constraint for cargo 3. (Please follow the order these variables appeared in the objective function.) (Click to select) v + (4) Write the compartment space capacity constraint for the Back compartment. (Please follow the order these variables appeared in the objective function.) (Click to select) v + + (5) There are constraints to maintain the weight distribution among the three compartments as 12:18:10. However, instead of using the proportion to the total weight, we can use two constraints, the first regulate the weight ratio between Compartment F and Compartment Center, and the second Compartamnet Front to Compartment Back. This way, each constraints only involve 8 variables instead of having all 12 variables appeared in one constraints. Write the constraint that regulate the weight ratio between the front and the center compartments. (move all variables to one side of the equation and leave the RHS as 0)