Shale Oil refinery blends two petroleum stocks, A and B, to produce two high-octane gasoline products, I and II. Stocks A and B are produced at the maximum rates of 450 and 700 bbl/hr, respectively. The corresponding octane numbers are 98 and 89, and the vapor pressures are 10 and 8 lb/in2. Gasoline I and gasoline II must have octane numbers of at least 91 and 93, respectively. The vapor pressure associated with both products should not exceed 12 lb/in2. The profits per bbl of I and II are $7 and $10, respectively.

Develop an LP model to determine the optimum production rate for I and II and their blend ratios from stocks A and B, and find the solution using AMPL, Solver, or TORA.

(Hint: Vapor pressure, like the octane number, is the weighted average of the vapor pressures of the blended stocks.)