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 17PT
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)=4x3y .

  5y34x+y42x+y5

Expert Solution & Answer
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Answer to Problem 17PT

The coordinates of the feasible region are (0,5),(4,3) and (2,3) . The maximum value of the function is 17 which occurs at (2,3) . The minimum value of the function is 15 which occurs at (0,5) .

  Algebra 2, Chapter 3, Problem 17PT , additional homework tip  1

Explanation of Solution

Given information:

The system of inequalities,

  5y34x+y42x+y5

Calculation:

Consider the system of inequalities,

  5y34x+y42x+y5

Plot the inequalities 5y3 , 4x+y4 and 2x+y5 on the coordinate plane.

  Algebra 2, Chapter 3, Problem 17PT , 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 (0,5),(4,3) and (2,3) is the feasible region.

Now, substitute each of the vertices in the function f(x,y)=4x3y to compute the maximum and minimum value of the function.

Value of the function at the vertex (0,5) ,

  f(0,5)=4(0)3(5)=15

Value of the function at the vertex (4,3) ,

  f(4,3)=4(4)3(3)=16+9=7

Value of the function at the vertex (2,3) ,

  f(2,3)=4(2)3(3)=8+9=17

Therefore, the maximum value of the function is 17 which occurs at (2,3) . The minimum value of the function is 15 which occurs at (0,5) .

Chapter 3 Solutions

Algebra 2

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