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 unitsof 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 totalrevenue that can be obtained?(Simplify your answer.)WoodChairRockerChaise lounge 1 unitPlastic Aluminum1 unit2 units3 units1 unit2 units1 unit1 unit5 unitsEnter your answer in the answer box.FEBLEGO23MacBook Air

Name: A company manufactures three types of patio furniture: chairs, rocker
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Description: 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

Answered: A company manufactures three types of…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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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.
FEB
LEGO
23
MacBook Air

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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