A ship has a single cargo hold which has a weight capacity of $70,000$ pounds and a volume capacity of $30,000$ cubic feet. The shipowner has contracted to carry loads of packaged beef. The total weight of the available beef is $65,000$ pounds; the total weight of the available grain is $75,000$ pounds. The volume per mass of the beef is $0\mathrm{.}2$ cubic foot per pound, and the volume per mass of the grain is $0\mathrm{.}4$ cubic foot per pound. The profit for shipping beef is $$0\mathrm{.}35$ per pound, and the profit for shipping grain is $$0\mathrm{.}12$ per pound. The shipowner is free to accept all or part of the available cargo; he wants to know how much meat and grain to accept in order to maximize profit.