1.Sunco Oil manufactures three types of unleaded gasoline

| August 30, 2017

Question
Sunco Oil manufactures three types of unleaded gasoline (super, premium, and regular). Each type pf gasoline is produced by blending together three types of drude oil (Crude 1, Crude 2, and Crude 3). The sales price per barel of gasoline and the purchase price per barrel or crude oil for the planning period are given in Table 1. Sunco can purchse 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 thre types pf crude oil are given in Table 2. It costs $4.0 to transform on barrel of crude oil intto one barrel of gasoline. Sunco’s refinery can produce a maximum of 14,000 barrels of gasoline daily.

Sunco has a contractual agreement wth some of its custoers 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 advertosing to stimulate demand for its products. Each dollar spent daily in advertising a particular gasoling increases the demand for that type of gasoline by ten barrels. For eslample, if Sunco decides to spend $20 dauly in advertising its super gasoline, the daily demand for super gasoline will increase by 20(10) – 200 barells. Assume that when transformed, one barrel of crude yeilds 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

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TABLE 1 – GAS AND CRUDE OIL PRICES

Sales Price

Purchase Price

Per Barrel

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

Sulfur

Rating

Content

Crude 1

12

0.5%

Crude 2

6

2.0%

Crude 3

8

3.0%

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