Question

A furniture manufacturer produces chairs and sofas. The chairs require 20 feet of wood, 1 lb. of foam rubber, and 2 square yards of material. The sofas require 100 feet of wood, 50 Ibs. of foam rubber, and 20 square yards of material. The manufacturer has in stock 1900 feet of wood, 500 Ibs. of foam rubber, and 240 square yards of material. If the chairs can be sold for $20 each and the sofas for $300 each, how many of each should be produced to maximize the income?

Answer 1

In order to maximize profit of $3700 we need to produce 50 units of Chairs and 9 units of Sofa

Explanation:

Let X be the number of units of Chairs produced and Y be the number of units of Sofa to be produced

wood foam rubber square yards of material Selling Price

Chairs 20X 1X 2X = $20X

Sofa 100Y 50Y 20Y = $300Y

1900 500 240

20x+100y=1900

x+50y=500

2x+20y=240

use equation 2 to find the value of x

x= 500-50y

Substitute value of x in equation 3

2(500-50y) + 20y= 240

1000-100y + 20y = 240

1000-240 = 100y-20y

760 = 80y

y= 9.5 ≈ 9 units ( since we can't make half of any product )

Put value of y in equation 2

x= 500- 50 ( 9)

x= 50 units

Maximize profit = 20X + 300Y

= 20(50) + 300( 9)

= $3700