Sunco Oil

Sunco Oil manufactures three types of gasoline (gas 1, gas 2 and gas 3). Each type is produced by blending three types of crude oil (crude 1, crude 2 and crude 3). The sales price per barrel of gasoline and the purchase price per barrel of crude oil are given in following table:
  Sales price per barrel   Purchase price per barrel
Gas 1 $70 Crude 1 $45
Gas 2 $60 Crude 2 $35
Gas 3 $50 Crude 3 $25

Sunco can purchase up to 5000 barrels of each type of crude oil daily.

The three types of gasoline differ in their octane rating and sulfur content. The crude oil blended to form gas 1 must have an average octane rating of at least 10 and contain at most 1% sulfur. The crude oil blended to form gas 2 must have an average octane rating of at least 8 and contain at most 2% sulfur. The crude oil blended to form gas 3 must have an octane rating of at least 6 and contain at most 1% sulfur. The octane rating and the sulfur content of the three types of oil are given in following table:

  Octane rating Sulfur content
Crude 1 12 0.5%
Crude 2 6 2.0%
Crude 3 8 3.0%

It costs $4 to transform one barrel of oil into one barrel of gasoline, and Sunco's refinery can produce up to 14,000 barrels of gasoline daily.

Sunco's customers require the following amounts of each gasoline: gas 1-3000 barrels per day; gas 2-2000 barrels per day; gas 3-1000 barrels per day. The company considers it an obligation to meet these demands. Sunco also has the option of advertising to stimulate demand for its products. Each dollar spent daily in advertising a particular type of gas increases the daily demand for that type of gas by 10 barrels. For example, if Sunco decides to spend $20 daily in advertising gas 2, the daily demand for gas 2 will increase by 20(10) = 200 barrels. Formulate an LP that will enable Sunco to maximize daily profits (profits = revenues - costs)





Material by Cliff Stein, used with permission.