Algebra: Structure And Method, Book 1
Algebra: Structure And Method, Book 1
(REV)00 Edition
ISBN: 9780395977224
Author: Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher: McDougal Littell
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Chapter 10.8, Problem 1E

a.

To determine

Draw the graph of the solution set of system.

a.

Expert Solution
Check Mark

Answer to Problem 1E

  Algebra: Structure And Method, Book 1, Chapter 10.8, Problem 1E , additional homework tip 1

Explanation of Solution

Given information:

  x≥2y+4x+y≥−24x+y≤4

Calculation:

The graph of,

  x≥2y+4x=2y+4  as  a  solid  line

The graph of x≥2y+4 is closed half plane shaded below the graph line x=2y+4 .

  x+y=−2  as  a  solid  linex+y≥−2  is  closed  half  plane

Shaded above the graph line x+y=−2   .

  4x+y=4  as  a  solid  line

  4x+y≤4 is closed half plane shaded below the graph line 4x+y=4 .

The graph of the system is as drawn.

  Algebra: Structure And Method, Book 1, Chapter 10.8, Problem 1E , additional homework tip 2

Hence, the graph is plotted.

b.

To determine

Find the corner point of the solution set.

b.

Expert Solution
Check Mark

Answer to Problem 1E

  (43,−43) , (2,−4),(0,−2)

Explanation of Solution

Given information:

  x≥2y+4x+y≥−24x+y≤4

Calculation:

The points where the boundary lines intersects.

These are

  (43,−43) , (2,−4),(0,−2) .

c.

To determine

Find the maximum and minimum value of 4x+7y .

c.

Expert Solution
Check Mark

Answer to Problem 1E

  −4,−14,−20

Explanation of Solution

Given information:

  x≥2y+4x+y≥−24x+y≤4

Calculation:

It must occur at a corner point of the accessible shaded region.

Now the value of 4x+7y at each corner point,

  (43,−43)  corner  point4(43)+7(−43)=−123=−4(2,−4)  corner  point4(2)+7(−4)=−20(0,−2)  corner  point4(0)+7(−2)=−14

Hence, the maximum and minimum value of 4x+7y is.

  −4,−14,−20

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Chapter 10.8, Problem 3ST
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Chapter 10.8, Problem 2E

Chapter 10 Solutions

Algebra: Structure And Method, Book 1

Ch. 10.1 - Prob. 1OECh. 10.1 - Prob. 2OECh. 10.1 - Prob. 3OECh. 10.1 - Prob. 4OECh. 10.1 - Prob. 5OECh. 10.1 - Prob. 6OECh. 10.1 - Prob. 7OECh. 10.1 - Prob. 8OECh. 10.1 - Prob. 9OECh. 10.1 - Prob. 10OE
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