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 0.2 cubic foot per pound, and the volume per mass of the grain is 0.4 cubic foot per pound. The profit for shipping beef is $0.35 per pound, and the profit for shipping grain is $0.12 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.
Linear Programming Model
Objective Function (Max or Min):
subject to
Volume:
Weight Capacity
Beef Weight
Grain Weight
Non-negativity
Optimal Solution:
Beef =
Grain =
Profit = $