Algebra 2
Algebra 2
1st Edition
ISBN: 9780078884825
Author: McGraw-Hill/Glencoe
Publisher: Glencoe/McGraw-Hill School Pub Co
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Chapter 3, Problem 27SGR
To determine

To calculate: The number of shoes manufactured to maximize the profit.

Expert Solution & Answer
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Answer to Problem 27SGR

The profit is $480. The company should manufacture 12 outdoor shoes and 16 indoor shoes.

Explanation of Solution

Given information:

Each pair of outdoor shoe require 2 hour in step 1 and 1 hour in step 2 and gives a profit of $20. Each pair of indoor shoe require 1 hour in step 1 and 3 hour in step 2 and gives a profit of $15.

40 hours of labor available for step 1 and 60 hours of labor is available for step 2 process.

Calculation:

Consider the provided information thateach pair of outdoor shoe require 2 hour in step 1 and 1 hour in step 2 and gives a profit of $20. Each pair of indoor shoe require 1 hour in step 1 and 3 hour in step 2 and gives a profit of $15.

40 hours of labor available for step 1 and 60 hours of labor is available for step 2 process.

Let x denote the number of outdoor shoes and y denote the number of indoor shoes.

Since, each pair of outdoor shoe require 2 hour in step 1 and 1 hour in step 2 and gives a profit of $20. Each pair of indoor shoe require 1 hour in step 1 and 3 hour in step 2 and gives a profit of $15.

  2x+y40x+3y60

And,

  x0y0 .

Plot the inequalities and shade the common region 2x+y40,x+3y60,x0 and y0

  Algebra 2, Chapter 3, Problem 27SGR

The profit function that is to be maximized is f(x,y)=20x+15y .

Substitute the vertices of the feasible region to find the point at which maximum revenue is there.

Substitute (0,0) in the function f(x,y)=20x+15y .

  f(0,0)=0

Substitute (12,16) in the function f(x,y)=20x+15y .

  f(12,16)=480

Substitute (20,0) in the function f(x,y)=20x+15y .

  f(20,0)=400

Substitute (0,20) in the function f(x,y)=20x+15y .

  f(0,20)=300

Since, maximum profit is $480. The company should manufacture 12 outdoor shoes and 16 indoor shoes.

Chapter 3 Solutions

Algebra 2

Ch. 3.1 - Prob. 2CYUCh. 3.1 - Prob. 3CYUCh. 3.1 - Prob. 4CYUCh. 3.1 - Prob. 5CYUCh. 3.1 - Prob. 6CYUCh. 3.1 - Prob. 7CYUCh. 3.1 - Prob. 8CYUCh. 3.1 - Prob. 9CYUCh. 3.1 - Prob. 10CYUCh. 3.1 - Prob. 11CYUCh. 3.1 - Prob. 12CYUCh. 3.1 - Prob. 13PPSCh. 3.1 - Prob. 14PPSCh. 3.1 - Prob. 15PPSCh. 3.1 - Prob. 16PPSCh. 3.1 - Prob. 17PPSCh. 3.1 - Prob. 18PPSCh. 3.1 - Prob. 19PPSCh. 3.1 - Prob. 20PPSCh. 3.1 - Prob. 21PPSCh. 3.1 - Prob. 22PPSCh. 3.1 - Prob. 23PPSCh. 3.1 - Prob. 24PPSCh. 3.1 - Prob. 25PPSCh. 3.1 - Prob. 26PPSCh. 3.1 - Prob. 27PPSCh. 3.1 - Prob. 28PPSCh. 3.1 - Prob. 29PPSCh. 3.1 - Prob. 30PPSCh. 3.1 - Prob. 31PPSCh. 3.1 - Prob. 32PPSCh. 3.1 - Prob. 33PPSCh. 3.1 - Prob. 34PPSCh. 3.1 - Prob. 35PPSCh. 3.1 - Prob. 36PPSCh. 3.1 - Prob. 37PPSCh. 3.1 - Prob. 38PPSCh. 3.1 - Prob. 39PPSCh. 3.1 - Prob. 40PPSCh. 3.1 - Prob. 41PPSCh. 3.1 - Prob. 42HPCh. 3.1 - Prob. 43HPCh. 3.1 - Prob. 44HPCh. 3.1 - Prob. 45HPCh. 3.1 - Prob. 46HPCh. 3.1 - Prob. 47HPCh. 3.1 - Prob. 48HPCh. 3.1 - Prob. 49HPCh. 3.1 - 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