The owner of a private freighter 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 up to 15 tons of cargo A, which takes up 675 cubic feet per ton and earns revenue of $85 per ton. Or, he may carry up to 54 tons of cargo B, with a volume of 450 cubic feet per ton and 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. 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?