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Problem 9-15 (Algorithmic) Bay Oil produces two types of fuels (regular and super) by mixing three...

  1. Problem 9-15 (Algorithmic)

    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 92 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 are shown in the following table. Likewise, the maximum demand for each end product and the revenue generated per barrel are shown.

    Input Cost/Barrel Octane Available (barrels)
    1 $16.5 95 140000
    2 $15 86 325000
    3 $15.5 105 300000
    Revenue/Barrel Max Demand (barrels)
    Regular $18.5 320000
    Super $20 450000

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

    Let Ri = the number of barrels of input i to use to produce Regular, i=1,2,3
    Si = the number of barrels of input i to use to produce Super, i=1,2,3

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

    Max _R1 + _R2 + _R3 + _S1 + _S2 + _S3
    s.t.
    _R1 + _S1 ≤ _
    _R2 + + _S2 ≤ _
    _R3 + S3 ≤ _
    _R1 + _R2 + _R3 ≤ _
    _S1 + _S2 + _S3 ≤ _
    _R1 + _R2 + _R3 ≥ _R1 + _R2 + _R3
    _S1 + _S2 + _S3 ≥ _S1 + _S2 + _S3

    R1, R2, R3, S1, S2, S3 ≥ 0

    What is the optimal contribution to profit? _

    Maximum Profit = _$   by making _ barrels of Regular and _ barrels of Super.

math   Statistics-And-Probability   
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Answer #1

Max z
= (R1+ R2 + R3) 18.5 + (S1 +S 2 + S3)*20 -
16.5 (R1 + S1) - 15 (R2 + S2) - 15.5 (R3 + S3)

2 R1 + 3.5 R2 + 3 R3 + 3.5 S1 + 5 S2 + 4.5 S3
CONSTRAINTS

R1 + S1 <= 140000
R2 + S2 <= 325000
R3 + S3 <= 300000

R1+R2 + R3 <= 320000
S1 + S2 + S3 <= 450000

95 R1 + 86 R2 + 105 R3 >= 92(R1 + R2 + R3)
95 S1 + 86 S2 + 105 S3 >= 100(S1 + S2 +S3)

2 _R1 3.5 _R2 3 _R3 3.5 _S1 5 _S2 4.5 _S3
s.t.
1 _R1 1 _S1 ≤ 140000
1 _R2 + 1 _S2 ≤ 325000
1 _R3 1 S3 ≤ 300000
1 _R1 1 _R2 1 _R3 ≤ 320000
1 _S1 1 _S2 1 _S3 ≤ 450000
95 _R1 86 _R2 105 _R3 ≥92 _R1 92 _R2 92 _R3
95 _S1 86 _S2 105 _S3 ≥100 _S1 100 _S2 100 _S3
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