An oil company distills two types of crude oil, A and B, to produce regular and premium gasoline and jet fuel. There are limits on the daily availability of crude oil and the minimum demand for the final products. If the production is not sufficient to cover demand, the shortage must be made up from outside sources at a penalty. Surplus production will not be sold immediately and will incur storage cost. The following table provides the data of the situation:

Develop an LP model to determine the optimal product mix for the refinery, and find the solution using AMPL, Solver, or TORA.

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Crude Crude A Crude B Demand (bbl/day) Revenue ($/bbl) Storage cost for surplus production ($/bbl) Penalty for unfilled demand ($/bbl) Fraction yield per bbl Regular .20 25 500 50 2 10 Premium .1 .3 700 70 3 15 Jet .25 .10 400 120 4 20 Price/bbl ($) 30 40 bbl/day 2500 3000