3.4-13.* A cargo plane has three compartments for storing cargo: front, center, and aft. These compartments have load capacity limits both in terms of weight and space, as summarized below: compartment weight capacity (t) volume capacity (ft) front 12 7,000 center 18 9,000 back 10 5,000 In addition, the weight of the cargo in the respective compartment must be in the same proportion as the weight capacity of that compartment to maintain the balance of the aircraft. The following four loads will be loaded onto an upcoming flight once space becomes available: charge weight (t) volume (feet 3/t) profit (US$/t) 1 20 500 320 N 16 700 400 3 25 600 360 4 4 13 400 290 Any portion of these charges can be accepted. The objective is to determine how much (if any) of each cargo should be accepted and how to distribute each cargo among the compartments in order to maximize the total profit per flight. (a) Formulate a linear programming model for this problem. (b) Solve this model by the simplex method to find one of several optimal solutions