Algebra 2
Algebra 2
1st Edition
ISBN: 9780078884825
Author: McGraw-Hill/Glencoe
Publisher: Glencoe/McGraw-Hill School Pub Co
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Chapter 3.4, Problem 18PPS
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)=8x3y.

  5y17y3x+19y4x+15

Expert Solution & Answer
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Answer to Problem 18PPS

The coordinates of the feasible region are (5,5) and (8,17) . The minimum value of the function is 55 which occurs at (5,5) . There is no maximum value of the function.

  Algebra 2, Chapter 3.4, Problem 18PPS , additional homework tip  1

Explanation of Solution

Given information:

The system of inequalities,

  5y17y3x+19y4x+15

Calculation:

Consider the system of inequalities,

  5y17y3x+19y4x+15

Plot the inequalities 5y17,y3x+19 and y4x+15 on the coordinate plane.

  Algebra 2, Chapter 3.4, Problem 18PPS , 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 (5,5) and (8,17) is the feasible region.

Now, substitute each of the vertices in the function f(x,y)=8x3y to compute the maximum and minimum value of the function.

Value of the function at the vertex (5,5) ,

  f(5,5)=8(5)3(5)=40+15=55

Value of the function at the vertex (8,17) ,

  f(8,17)=8(8)3(17)=64+51=115

In the region there is a point say (15,10) which yields a maximum value then 115.

Therefore, the minimum value of the function is 55 which occurs at (5,5) . There is no maximum value of the function.

Chapter 3 Solutions

Algebra 2

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