Ri Si: Ingredient Cost/Barrel Octane Available (Barrels) [PDF]

Zitiervorschau

Bay Oil produces two types of fuel (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, whereas super must have a level of at least 100. The cost per barrel, octane levels, and available amounts (in barrels) for the upcoming twoweek period appear in the following table, along with the maximum demand for each end product and the revenue generated per barrel. Ingredient

Cost/Barrel

Octane

Available (barrels)

1

$16.50

100

150,000

2

$14.00

87

390,000

3

$17.50

110

340,000

Revenue/Barrel

Max Demand (barrels)

Regular

$18.50

390,000

Super

$20.00

540,000

Develop and solve a linear programming model to maximize contribution to profit. (Assume Ri is the amount of ingredient i used in producing regular, and Si is the amount of ingredient i used in producing Super. Use the units of barrels and dollars for all answers.) Max s.t.Input 1 Capacity Input 2 Capacity Input 3 Capacity Max Demand for Regular Max Demand for Super Required Octane Level, Regular Required Octane Level, Super R1, R2, R3, S1, S2, S3 ≥ 0 What is the optimal contribution to profit? Report your values for R1, R2, R3, S1, S2, S3. (R1, R2, R3, S1, S2, S3) = What is the maximum profit (in dollars)?