BLENDING—OIL REFINING. California Oil Company (Caloco) produces two grades of unleaded gasoline (regular and premium) from three raw crudes (Pacific, Gulf, and Middle East). The current octane rating,...

BLENDING—OIL REFINING. California Oil Company (Caloco) produces two grades of unleaded gasoline (regular and premium) from three raw crudes (Pacific, Gulf, and Middle East). The current octane rating, the availability (in barrels), and the cost per barrel for a given production period are given in the following table.

For this period, Caloco has contracts calling for a minimum of 2 0 0 ,0 0 0 gallons of regular and 1 0 0 ,0 0 0 gallons of premium gasoline, and it has a refining capacity of 400,000 total gallons.

 (A barrel is 42 gallons.) Caloco sells regular gasoline to retailers for $0.52 and premium gasoline for $0.60 per gallon. To be classified as “regular,” the refined gas must have an octane rating of 87 or more; premium must have an octane rating of 91 or more. Assume that the octane rating of any mixture is the weighted octane rating of its components.

 a. Solve for the optimal amount of each crude to blend into each gasoline during this production period.