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 18PT
To determine

To calculate: The coordinates of the feasible region when the provided system of inequalities are graphed. Also evaluate the minimum and maximum value of the function f(x,y)=2x+y .

  x≥−101≥y≥−63x+4y≤−82y≥x−10

Expert Solution & Answer
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Answer to Problem 18PT

The coordinates of the feasible region are (−10,−6),(−2,−6),(2.4,−3.8),(−4,1) and (−10,1) . The maximum value of the function is 1 which occurs at (2.4,−3.8) . The minimum value of the function is −26 which occurs at (−10,−6) .

  Algebra 2, Chapter 3, Problem 18PT , additional homework tip 1

Explanation of Solution

Given information:

The system of inequalities,

  x≥−101≥y≥−63x+4y≤−82y≥x−10

Calculation:

Consider the system of inequalities,

  x≥−101≥y≥−63x+4y≤−82y≥x−10

Plot the inequalities x≥−10,1≥y≥−6,3x+4y≤−8 and 2y≥x−10 on the coordinate plane.

  Algebra 2, Chapter 3, Problem 18PT , additional homework tip 2

The feasible region is the region that is common to all the three inequalities.

Therefore, the region bounded by the vertices (−10,−6),(−2,−6),(2.4,−3.8),(−4,1) and (−10,1) is the feasible region.

Now, substitute each of the vertices in the function f(x,y)=2x+y to compute the maximum and minimum value of the function.

Value of the function at the vertex (−10,−6) ,

  f(−10,−6)=2(−10)−6=−26

Value of the function at the vertex (−2,−6) ,

  f(−2,−6)=2(−2)−6=−10

Value of the function at the vertex (2.4,−3.8) ,

  f(2.4,−3.8)=2(2.4)−3.8=1

Value of the function at the vertex (−4,1) ,

  f(−4,1)=2(−4)+1=−7

Value of the function at the vertex (−10,1) ,

  f(−10,1)=2(−10)+1=−19

Therefore, the maximum value of the function is 1 which occurs at (2.4,−3.8) . The minimum value of the function is −26 which occurs at (−10,−6) .

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Chapter 3 Solutions

Algebra 2

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