solution

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 two-week 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 $16.50 100 160,000

2 $14.00 87 400,000

3 $17.50 110 350,000

Revenue/Barrel Max Demand (barrels)

Regular $18.50 400,000

Super $20.00 550,000

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)?