Bay Oil produces two types of fuels (regular and super) by mixing three ingredie

Question

Bay Oil produces two types of fuels (regular and super) by mixing three ingredients. The major distinguishing feature of the two products is the octane level required. Regular fuel must have a minimum octane level of 90 while super must have a level of at least 100. The cost per barrel, octane levels and available amounts (in barrels) for the upcoming two-week period appear in the table below. Likewise, the maximum demand for each end product and the revenue generated per barrel are shown below.

Develop and solve a linear programming model to maximize contribution to profit.

If required, round your answers to one decimal place. For subtractive or negative numbers use a minus sign even if there is a + sign before the blank. (Example: -300)...

So far I have,

Please explain how to fill out the rest of the table data.

Ingredient Cost/Barrel Octane Available (barrels) 1 $16.50 100 110,000 2 $14.00 87 350,000 3 $17.50 110 300,000 S3 Max R3 110000 350000 300,000 350,00o 500,000 R3 R2 S3 R3 00 S3 90 90 110 R3 90 87 100 100 s, 100 S2 100 S1 R1, R2, R3,S1,S2, S3 2 0

Explanation / Answer

Objective: to maximize the profit (Revenue-cost).

Constrains:

The availability of 3 ingredients are 110000, 350000, 300000 respectively.

The Max demands forthe two fuels are 350000 and 500000 respectively.

Octane must exceed 90 and 100 respectivelyin the two fuels.

Decision variables:

R1: amount of ingredient 1 for regular fuel.

R2: amount of ingredient 2 for regular fuel.

R3: amount of ingredient 3 for regular fuel.

S1: amount of ingredient 1 for super fuel.

S2: amount of ingredient 2 for super fuel.

S3: amount of ingredient 3 for super fuel.

Objective:

Maximize 18.5(R1 + R2 +R3) + 20(S1+S2+S3) -16.5(R1 +S1) -14(R2+S2) -17.5(R3+S3)

Maximize 2*R1 + 4.5*R2 +1*R3 +3.5*S1 +6*S2 +2.5*S3

Constraints:

R1 +S1 110000

R2 + S2 350000

R3 + S3 300000

R1 + R2 +R3 350000

S1+S2+S3 500000

100R1 + 87R2 + 110R3 90R1 + 90R2 + 90R3

100S1+ 87S2+ 110S3 100S1+ 100S2+ 100S3

R1, R2 ,R3, S1,S2,S3 0

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