Problem B (50 points) A cargo airplane has three compartments for storing cargo: front, center, and back. These compartments have capacity limits on both weight and space, as summarized in Table 1. Four cargoes have been offered for shipping on an upcoming flight as space is available. Their unit weight, volume, and profit information is listed in Table 2. In order to meet the shipping contract requirements, at least a total of 55 units of these four cargoes must be loaded on the plane. Any portion of these cargoes can be accepted for shipping. Due to product mix requirements, Cargo Bs quantity must be no more than Cargo Cs quantity. The managerial goal is to determine how many units (if any) of each cargo should be accepted and loaded on the cargo airplane in its three compartments to maximize the total shipping profit for one flight. List your linear program for this problem. Make sure your decision variables are clearly defined and the objective function and its constraints are listed. You do not need to solve the program.

Table 1.

Compartment	Weight Capacity (tons)	Space Capacity (Cubic Feet)
Front	180	2000
Center	250	4200
Back	155	3100

Table 2.

Cargo	Unit Weight (ton)	Volume (cubic feet per unit)	Shipping Profit per unit
A	10	90	$170
B	7	200	$190
C	15	150	$210
D	8	120	$255