When gasoline is refined from crude oil, each gallon of regular, mid-grade, and premium uses a different blend of two different grades of crude oil according to the following matrix.

In addition, the demand (in thousands of gallons) from a Houston refinery is 22 regular, 12 mid-grade, and 8 premium, and the demand from a Gulfport refinery is 30 regular, 20 mid-grade, and 11 premium.
(a) Make a 2 × 3 matrix B that contains the blending information and a 3 × 2 matrix D for the demands at each refinery. Then use a matrix product to find each refinery's need for each type of crude oil.
(b) If the cost of black crude is $3.17 per gallon and for gold crude is $3.32 per gallon, then the matrix
P = [3.17 3.32]
Represents these crude prices. Write a matrix product involving B, D, and P that could be used to find the total cost for crude oil at each refinery.
Then find those total costs?

Transcribed Image Text:

Gasoline Blends Mid. Reg. Prem. Crude Grade 2 Black 4 Gold Nn mjin