Problem:
Space Constrained Inventories
A grocer has exactly 1,000 square feet available to display and sells 3 kinds of vegetables. The space consumed by each kind of vegetable is proportional to its cost, and tomatoes consume 0.5 square feet per pound. There is a $100 setup cost for replenishing any of the vegetables, and the interest rate is 25% per annum. The 3 vegetables for sale have the following data:
Tomatoes: annual demand is 850 pounds and the cost per pound is $0.29.
Lettuce: annual demand is 1280 pounds and the cost per pound is $0.45.
Zucchini: annual demand is 630 pounds and the cost per pound is $0.25.
What is the optimal quantity for purchasing each vegetable?