Carrington Oil produces gas 1 and gas 2 from two types of crude oil: crude 1 and crude 2. Gas 1 is allowed to contain up to 4% impurities, and gas 2 is allowed to contain up to 3% impurities. Gas 1 sells for $72 per barrel, whereas gas 2 sells for $84 per barrel. Up to 4200 barrels of gas 1 and up to 4300 barrels of gas 2 can be sold. The cost per barrel of each crude, their availability, and the level of impurities in each crude are listed in the file P04_71.xlsx. Before blending the crude oil into gas, any amount of each crude can be “purified” for a cost of $3.50 per barrel. Purification eliminates half of the impurities in the crude oil.

a. Determine how to maximize profit.

b. Use SolverTable to determine how an increase in the availability of crude 1 affects the optimal profit.

c. Use SolverTable to determine how an increase in the availability of crude 2 affects the optimal profit.

d. Use SolverTable to determine how a change in the price of gas 2 changes the optimal profit and the types of gas produced.