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Linear Programming

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Riverside oil company in eastern Kentucky produces 3 different grades of gasoline. They are regular, premium, and supreme grades. Each barrel of regular grade sells for $77 while premium grade sells for $82 per barrel and supreme grade sells for $89 per barrel. Petroleum component A, B and C are purchased to be blended together for the production of three different grades of gasoline. The availability and costs of petroleum components A, B, and C are: A: 8000 barrels available at $32 cost per barrel; B: 7000 barrels available at $45 cost per barrel; C: 9000 barrels available at $39 cost per barrel.

The following constraints/blending specifications apply: Regular: at 30% of A; no more than 30% of B; no restriction on C

Premium: at least 25% of B; no restriction on A and C

Supreme: no more than 25% of A; no restriction on B; at least 40% on C.

a. List the linear program for this problem.
b. Report optimal way to blend these three petroleum components for production.
c. What is the maximized profit?

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