An oil refinery produces two products: jet fuel and gasoline. The profit for the refinery is $0.10 per barrel for jet fuel and $0.20 per barrel for gasoline. The following conditions must be met:

I) Only 10,000 barrels of crude oil are available for processing.

II) The refinery has a government contract to produce at least 1,000 barrels of jet fuel.

III) The refinery has a private contract to produce at least 2,000 barrels of gasoline.

The refinery wants to know how much of each product should be produced for maximum profit.

a) Define your decision variables as accurately as possible.

b) What is the objective function of the problem?

c) Write down three constraints addressing requirements I), II), and III).

d) Write down another constraint that guarantees for every barrel of jet fuel, at most three barrels of gasoline are produced.