Question $1$: $($total $90$ points in two parts$)$ The owner of a private freighter company is trying to decide which cargo he should carry on his next trip. He has two choices of cargo, which he can agree to carry in any combination. He may carry the following:

up to $15$ tons of cargo $A,$ with a volume of $675$ cubic feet per ton and earns revenue of $$85$ per ton

up to $54$ tons of cargo B$,$ with a volume of $450$ cubic feet per ton and earns revenue of $$79$ per ton.

The freighter is divided into two holds, starboard and port. The starboard hold has a volume of $14,000$ cubic feet and a weight capacity of $26$ tons. The port hold has a volume of $15,400$ cubic feet and a weight capacity of $32$ tons. For steering reasons, it is necessary that the weight be distributed equally between the two sides of the freighter. However, the freighter engines and captain's bridge, which together weight $6$ tons, are on the starboard side of the freighter and should count toward equal weighting. This means that the port side is usually loaded with $6$ tons more cargo to equalize the weight. The owner may carry any combination of the two cargoes in the same hold without a problem. How should this freighter be loaded to maximize total revenue?

a$.($worth $45$ points$)$

Formulate the LP model. Be sure to include and label all three parts of a good formulation.

b$.($worth another $45$ points$)$ Solve the LP problem using Excel Solver.

Please show solving on excel including the steps