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 2CYU
To determine

To calculate: The coordinates of the vertices of the feasible region formed by graphing the given inequalities y3x+6, yx and y3 . Also maximum and minimum values of the function f(x,y)=8x+4y in this region.

Expert Solution & Answer
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Answer to Problem 2CYU

The graph of the given system of inequalities is,

  Algebra 2, Chapter 3.4, Problem 2CYU , additional homework tip  1

The coordinates of the feasible region are A(1,3), B(3,3) and C(3,3) .

The maximum value of the function is 20 at (1,3) and minimum value of the function is 12 at (3,3) .

Explanation of Solution

Given information:

The inequalities y3x+6, yx and y3 and the function f(x,y)=8x+4y .

Formula used:

Linear programming is a technique to find the maximum and the minimum value of a given function over a given system of some inequalities, with each inequality representing a constraint. Graph the inequalities and obtain the vertices of the feasible region (solution set). Substitute the coordinates of the feasible region in the function and determine the maximum and the minimum value.

Calculation:

Consider the provided system of inequalities y3x+6, yx and y3 .

Recall that linear programming is a technique to find the maximum and the minimum value of a given function over a given system of some inequalities, with each inequality representing a constraint. Graph the inequalities and obtain the vertices of the feasible region (solution set).

Graph the given inequalities and locate the vertices of the feasible region.

  Algebra 2, Chapter 3.4, Problem 2CYU , additional homework tip  2

The feasible region is formed by the vertices A, B and C. The coordinates of the vertices of the feasible region are A(1,3), B(3,3) and C(3,3) .

Now, to find the maximum and minimum value of the function, substitute the coordinates of the feasible region in the function and determine the maximum and the minimum value.

So, substitute A(1,3), B(3,3) and C(3,3) in the function f(x,y)=8x+4y and evaluate the maximum and minimum value as,

  (x,y)8x+4yf(x,y)(1,3)8(1)+4(3)20(3,3)8(3)+4(3)12(3,3)8(3)+4(3)12

From the above table, it is observed that the maximum value of the function is 20 at (1,3) and minimum value of the function is 12 at (3,3) .

Thus, graph of the given system of inequalities is,

  Algebra 2, Chapter 3.4, Problem 2CYU , additional homework tip  3

The coordinates of the feasible region are A(1,3), B(3,3) and C(3,3) and the maximum value of the function is 20 at (1,3) and minimum value of the function is 12 at (3,3) .

Chapter 3 Solutions

Algebra 2

Ch. 3.1 - Prob. 2CYUCh. 3.1 - Prob. 3CYUCh. 3.1 - Prob. 4CYUCh. 3.1 - Prob. 5CYUCh. 3.1 - Prob. 6CYUCh. 3.1 - Prob. 7CYUCh. 3.1 - Prob. 8CYUCh. 3.1 - Prob. 9CYUCh. 3.1 - Prob. 10CYUCh. 3.1 - Prob. 11CYUCh. 3.1 - Prob. 12CYUCh. 3.1 - Prob. 13PPSCh. 3.1 - Prob. 14PPSCh. 3.1 - Prob. 15PPSCh. 3.1 - Prob. 16PPSCh. 3.1 - Prob. 17PPSCh. 3.1 - Prob. 18PPSCh. 3.1 - Prob. 19PPSCh. 3.1 - Prob. 20PPSCh. 3.1 - Prob. 21PPSCh. 3.1 - Prob. 22PPSCh. 3.1 - Prob. 23PPSCh. 3.1 - Prob. 24PPSCh. 3.1 - Prob. 25PPSCh. 3.1 - Prob. 26PPSCh. 3.1 - Prob. 27PPSCh. 3.1 - Prob. 28PPSCh. 3.1 - Prob. 29PPSCh. 3.1 - Prob. 30PPSCh. 3.1 - Prob. 31PPSCh. 3.1 - Prob. 32PPSCh. 3.1 - Prob. 33PPSCh. 3.1 - Prob. 34PPSCh. 3.1 - Prob. 35PPSCh. 3.1 - Prob. 36PPSCh. 3.1 - Prob. 37PPSCh. 3.1 - Prob. 38PPSCh. 3.1 - Prob. 39PPSCh. 3.1 - Prob. 40PPSCh. 3.1 - Prob. 41PPSCh. 3.1 - Prob. 42HPCh. 3.1 - Prob. 43HPCh. 3.1 - Prob. 44HPCh. 3.1 - Prob. 45HPCh. 3.1 - Prob. 46HPCh. 3.1 - Prob. 47HPCh. 3.1 - Prob. 48HPCh. 3.1 - Prob. 49HPCh. 3.1 - 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