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)=8x−3y.

  −5≥y≥−17y≤3x+19y≥−4x+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,

  −5≥y≥−17y≤3x+19y≥−4x+15

Calculation:

Consider the system of inequalities,

  −5≥y≥−17y≤3x+19y≥−4x+15

Plot the inequalities −5≥y≥−17,y≤3x+19 and y≥−4x+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)=8x−3y 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.

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Chapter 3.4, Problem 17PPS
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Chapter 3.4, Problem 19PPS

Chapter 3 Solutions

Algebra 2

Ch. 3.1 - Prob. 1ACYPCh. 3.1 - Prob. 1BCYPCh. 3.1 - Prob. 2ACYPCh. 3.1 - Prob. 2BCYPCh. 3.1 - Prob. 3CYPCh. 3.1 - Prob. 4ACYPCh. 3.1 - Prob. 4BCYPCh. 3.1 - Prob. 4CCYPCh. 3.1 - Prob. 4DCYPCh. 3.1 - Prob. 1CYU
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