Q$3-$a$)$ A cargo plane has three compartments for storing cargo: front, centre and rear. These compartments have the following fimits on both weight and space Compartment Weight capacity $($tonnes$)$ Space capacity $($cubic metres$)$ Front $106800$ Centre Rear $16870085300$A cargo plane has three compartments for storing cargo: front, centre and rear. These compartments

have the following limits on both weight and space:

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 plane. The following four

cargoes are available for shipment on the next flight:

Any proportion of these cargoes can be accepted. The objective is to determine how much $($if

any$)$ of each cargo $C1,C2,C3$ and $C4$ should be accepted and how to distribute each among the

compartments so that the total profit for the flight is maximized.

$($a$)$ Formulate the above problem as a linear program

$($b$)$ What assumptions are made in formulating this problem as a linear program?

$($c$)$ Briefly describe the advantages of using a software package to solve the above linear program,

over a judgmental approach to this problem.