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A company manufactures three types of patio furniture: chairs, rockers, and chaise The maximum total revenue that can be obtained is $. lounges. Each requires wood, plastic, and aluminum as given in the table below. The company has available 400 units of wood, 600 units of plastic, and 1500 units of aluminum. Each chair, rocker, and chaise lounge sells for $24, $32, and $48, respectively. Assuming that all furniture can be sold, what is the maximum total revenue that can be obtained? (Simplify your answer.) Wood 1 unit 1 unit Chaise lounge 1 unit 2 units Plastic Aluminum 1 unit 1 unit 2 units 3 units 5 units Chair Rocker

Linear Algebra: A Modern Introduction

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter2: Systems Of Linear Equations

Section2.4: Applications

Problem 3EQ: A florist offers three sizes of flower arrangements containing roses, daisies, and chrysanthemums....

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A company manufactures three types of patio furniture: chairs, rockers, and chaise The maximum total revenue that can be obtained is $.
lounges. Each requires wood, plastic, and aluminum as given in the table below.
The company has available 400 units of wood, 600 units of plastic, and 1500 units
of aluminum. Each chair, rocker, and chaise lounge sells for $24, $32, and $48,
respectively. Assuming that all furniture can be sold, what is the maximum total
revenue that can be obtained?
(Simplify your answer.)
Wood
Chair
Rocker
Chaise lounge 1 unit
Plastic Aluminum
1 unit
2 units
3 units
1 unit
2 units
1 unit
1 unit
5 units
Enter your answer in the answer box.
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Expert Solution

Step 1

Let $x_{1}, x_{2}, x_{3}$ denote the number of chairs, Rockers and Chaise lounge produced by the company. Since the number of furniture produced cannot be negative, $x_{1}, x_{2}, x_{3} \geq 0 .$

The number of units of wood produce $(x_{1})$ number of chairs, $(x_{2})$ number of Rockers, and $(x_{3})$ number of Chaise lounges respectively are $(1 x_{1})$ , $(1 x_{2})$ and $(1 x_{3})$ , so that the total number of units of wood used cannot be more than 400.

This gives an inequality of the form

$x_{1} + x_{2} + x_{3} \leq 400 .$

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