Sunco oil manufactures three types of unleaded gasoline

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Sunco Oil manufactures three types of unleaded gasoline (super, premium, and regular). Each type pf gasoline is produced by blending together 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 or crude oil for the planning period are given in Table 1. Sunco can purchase up to 5, 000 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 super gasoline must have an average octane rating of at least 10 and contain at most 1% sulfur. The crude oil blended to form premium must have an average octane rating of at least 8 and contain at most 2% sulfur. The crude oil blended to form regular gasoline must have an average octane rating of at least 6 and contain at most 1% sulfur. The octane rating and sulfur content of these three types of crude oil are given in Table 2. It costs $4.0 to transform on barrel of crude oil into one barrel of gasoline. Sunco’s refinery can produce a maximum of 14,000 barrels of gasoline daily.

 

Sunco has a contractual agreement with some of its customers to supply $3,000 barrels of super, 2,000 barrels of premium, and 1,000 barrels of regular gasoline daily. Sunco also has the option of advertising to stimulate demand for its products. Each dollar spent daily in advertising a particular gasoline increases the demand for that type of gasoline by ten barrels. For example, if Sunco decides to spend $20 daily in advertising its super gasoline, the daily demand for super gasoline will increase by 20(10) – 200 barrels. Assume that when transformed, one barrel of crude yields one barrel of gasoline. Formulate a linear programming model that will enable Sunco to maximize daily profits.

 

Please include Excel Solver spreadsheet and the formulation of the decision variable and objective function

 

TABLE 1 – GAS AND CRUDE OIL PRICES

Sales Price (Per Barrel)

Purchase Price (Per Barrel)

Super

$70

Crude 1

$45

Premium

$60

Crude 2

$35

Regular

$50

Crude 3

$25

TABLE 2 – OCTANE RATINGS AND SULFUR CONTENTS OF CRUDE OIL

 

Octane Rating

Sulfur Content

 

Crude 1

12

0.50%

 

Crude 2

6

2.00%

 

Crude 3

8

0.03