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)=4x−3y .

  5≥y≥−34x+y≤4−2x+y≤5

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,

  5≥y≥−34x+y≤4−2x+y≤5

Calculation:

Consider the system of inequalities,

  5≥y≥−34x+y≤4−2x+y≤5

Plot the inequalities 5≥y≥−3 , 4x+y≤4 and −2x+y≤5 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)=4x−3y 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) .

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Chapter 3 Solutions

Algebra 2

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