A Problem With Two Knapsack-Style Constraints

Business Decision Analytics Under Uncertainty

We are loading a vessel that can carry up to 300 tons of cargo, occupying up to 200 units of volume. We can load it with items of the following types:

Item Weight
(Tons)
Volume Number
Available
Profit if
Loaded
1 40 10 3 $ 800.00
2 8 12 10 $ 150.00
3 20 22 4 $ 300.00
4 15 5 5 $ 500.00


We can load multiple copies of each item, up to the "number available".  How many of each type of item should be loaded to maximize profit, without exceeding the weight and volume limits?