# Non linear Optimization

Ordering fuel. Three liquid fuels are stored in tanks for use in a blending process. Each fuel is characterized by a demand rate, a fixed replenishment cost, and a unit cost. Inventory carrying costs are assessed at the rate of 12 percent per year.

In order to save money on insurance rates, the operating policy is to limit the average value of stock on hand to no more than $7,500.

Fuel Demand Fixed Cost Unit Cost

1 1,000/year $100 $50

2 250/year $75 $100

3 500/year $50 $20

a. What are the optimal order quantities for the three items when they are ordered jointly, assuming that the fixed ordering costs are incurred for each item? What is the average annual cost for the three items combined?

b. Suppose the items are managed separately, but the overall limit on stock value still holds. What are the order quantities for the individual items? What is the average annual cost for the three items combined?

c. Suppose the stock limit in the base case is relaxed. If the limit is raised by $500, what is the impact on the optimal average annual costs?

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An attached Excel file contains formulas and explanations for finding optimal solutions to the given problems.