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 $16.50 100 170,000

2 $14.00 87 410,000

3 $17.50 110 360,000

Revenue/Barrel Max Demand (barrels)

Regular $18.50 410,000

Super $20.00 560,000

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)?$