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 $

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter3: Matrices

Section3.1: Matrix Operations

Problem 19EQ: A factory manufactures three products (doohickies, gizmos, and widgets) and ships them to two...

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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

Gold

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		$

Expert Solution

Step 1

Given Information's is as follows,

Gasoline Blends

Reg. Mild. Prem.

Crude Grade Black $\frac{3}{4}$ $\frac{2}{5}$ $\frac{1}{4}$

Gold $\frac{1}{4}$ $\frac{3}{5}$ $\frac{3}{4}$

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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