Algebra: Structure And Method, Book 1
Algebra: Structure And Method, Book 1
(REV)00 Edition
ISBN: 9780395977224
Author: Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher: McDougal Littell
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Chapter 10.8, Problem 2E
To determine

To find: The x and y that maximise the given problem.

Expert Solution & Answer
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Answer to Problem 2E

At x=2 and y=3 , R attains its maximum value.

Explanation of Solution

Given:

The problem is given as:

  maximize R=x+3yconstraints x≥2y≥1x+2y≤8x+y≤6

Calculation:

The value of x and y is calculated as:

The table for x+y=6 is given as:

    x06
    y60

The table for x+2y=8 is given as:

    x08
    y40

The graph of the above problem is given as:

  Algebra: Structure And Method, Book 1, Chapter 10.8, Problem 2E

As the feasible region is bounded, so the function R has the maximum and minimum both the value.

The corner points of above graphs are as:

  (2,3),(2,1),(5,1),(4,2)

In order to find the maximum value of function R , check the value for R at corner points is given as:

  x+3y=2+3(3)=11x+3y=2+3(1)=5

Further simplified as:

  x+3y=5+3(1)=8x+3y=4+3(2)=10

Therefore at x=2 and y=3 , R attains its maximum value.

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Chapter 10.8, Problem 1E
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Chapter 10.8, Problem 3E

Chapter 10 Solutions

Algebra: Structure And Method, Book 1

Ch. 10.1 - Prob. 1OECh. 10.1 - Prob. 2OECh. 10.1 - Prob. 3OECh. 10.1 - Prob. 4OECh. 10.1 - Prob. 5OECh. 10.1 - Prob. 6OECh. 10.1 - Prob. 7OECh. 10.1 - Prob. 8OECh. 10.1 - Prob. 9OECh. 10.1 - Prob. 10OE
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