When gasoline is refined from crude oil, each gallon of regular, midgrade, and premium uses a different blend of two different grades of crude oil according to the following matrix.     Gasoline Blends     Reg. Mid. Prem. Crude Grade Black 3 4 2 5 1 4   Gold 1 4 3 5 3 4 In addition, the demand (in thousands of gallons) from a Houston refinery is 23 regular, 11 midgrade, and 9 premium, and the demand from a Gulfport refinery is 31 regular, 21 midgrade, and 13 premium. (a) Make a 2 ✕ 3 matrix B that contains the blending information and a 3 ✕ 2 matrix D for the demands (in thousands of gallons) at each refinery. B =                                     D =                                     Use a matrix product to find each refinery's need for each type of crude oil.                             Houston needs  gallons of black crude and  gallons of gold crude. Gulfport needs  gallons of black crude and  gallons of gold crude. (b) If the cost of black crude is $1.12 per gallon and for gold crude is $1.52 per gallon, then the matrix P = [1.12   1.52] 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.                             Find those total costs. Houston's cost    $  Gulfport's cost    $

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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When gasoline is refined from crude oil, each gallon of regular, midgrade, and premium uses a different blend of two different grades of crude oil according to the following matrix.

    Gasoline Blends
    Reg. Mid. Prem.
Crude Grade Black
3
4
2
5
1
4
  Gold
1
4
3
5
3
4

In addition, the demand (in thousands of gallons) from a Houston refinery is 23 regular, 11 midgrade, and 9 premium, and the demand from a Gulfport refinery is 31 regular, 21 midgrade, and 13 premium.

(a) Make a 2 ✕ 3 matrix B that contains the blending information and a 3 ✕ 2 matrix D for the demands (in thousands of gallons) at each refinery.
B =
                 
                 
D =
           
           
           

Use a matrix product to find each refinery's need for each type of crude oil.
             
           
 

Houston needs  gallons of black crude and  gallons of gold crude. Gulfport needs  gallons of black crude and  gallons of gold crude.

(b) If the cost of black crude is $1.12 per gallon and for gold crude is $1.52 per gallon, then the matrix
P = [1.12   1.52]
represents these crude prices. Write a matrix product involving BD, and P that could be used to find the total cost for crude oil at each refinery.
             
           
 

Find those total costs.
Houston's cost   
Gulfport's cost   
Expert Solution
Step 1

Given Information's is as follows,

                                           Gasoline Blends

                                  Reg.             Mild.               Prem.

Crude Grade  Black    34                  25                     14

                       Gold    14                  35                      34

Also given that the demand from Houston refinery is 23 regular, 11 midgrade and 9 premium and the demand from a Gulfport refinery is 31 regular, 21 midgrade, and 13 premium.

 

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