4th Edition

ISBN: 9781337516853

Author: Larson

Publisher: CENGAGE CO

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Question

Chapter 7.6, Problem 50E

(a)

To determine

The maximum value at vertex A.

(a)

Expert Solution

Answer to Problem 50E

The function having the maximum value at A is Z=−x+2y

Explanation of Solution

Given:

The function having maximum value at vertex A(0,4)

Formula used:

The substituting the values based on the vertex values.

Calculation:

Given the set of objective functions and area determined by the constraints to find which of the objective function has got maximum/minimum values at certain vertices of the area.

The areas determined by the constraints given are as shown below,

EBK PRECALCULUS W/LIMITS, Chapter 7.6, Problem 50E

The functions given are:

(i) z=2x+y

(ii) z=2x−y

(iii) z=−x+2y

(a) To find the function having maximum value at vertex A(0,4)

(i)

Value of z=2x+y at A

Value of z=2(0)+4Value of z=4

(ii)

Value of z=2x−y at AValue of z=2(0)−4Value of z=−4

(iii)

value of z=−x+2y at AValue of z=−(0)+2(4)Value of z=8

The function having maximum value at A is z=−x+2y

Conclusion:

The function having maximum value at A is z=−x+2y

(b)

To determine

The maximum value at vertex B.

(b)

Expert Solution

Answer to Problem 50E

The maximum value at vertex B is z=2x+y

Explanation of Solution

Given:

The function having maximum value at vertex B(4,3)

Formula used:

The substituting the values based on the vertex values.

Calculation:

To find function having maximum value at vertex B(4,3)

(iv)

value of z=2x+y at BValue of z=2(4)+3Value of z=11

(v)

Value of z=2x−y at BValue of z=2(4)−3Value of z=5

(vi)

value of z=−x+2y at BValue of z=−(4)+2(3)Value of z=2

The function having maximum value at B is z=2x+y

Conclusion:

The function having maximum value at B is z=2x+y

(c)

To determine

To find:The maximum value at vertex C.

(c)

Expert Solution

Answer to Problem 50E

The maximum value at vertex C is z=2x+y and z=2x−y

Explanation of Solution

Given:

The function having maximum value at vertex C(5,0)

Formula used:

The substituting the values based on the vertex values.

Calculation:

To find function having maximum value at vertex C(5,0)

(viii)

value of z=2x+y at CValue of z=2(5)+0Value of z=10

(viiii)

Value of z=2x−y at CValue of z=2(5)−0Value of z=10

(iX)

value of z=−x+2y at CValue of z=−(5)+2(0)Value of z=−5

The function having maximum value at C is z=2x+y and z=2x−y

Conclusion:

The function having maximum value at C is z=2x+y and z=2x−y

(d)

To determine

The minimum value at vertex C.

(d)

Expert Solution

Answer to Problem 50E

The minimum value at vertex C is z=−x+2y

Explanation of Solution

Given:

The function having maximum value at vertex C(5,0)

Formula used:

The substituting the values based on the vertex values.

Calculation:

To find function having minimum value at vertex

From the part (c) it is clear that the function having minimum value at C is z=−x+2y

Conclusion:

The minimum value at C is z=−x+2y

Chapter 7.6, Problem 49E

Chapter 7.6, Problem 51E

Chapter 7 Solutions

EBK PRECALCULUS W/LIMITS

Ch. 7.1 - Prob. 1E Ch. 7.1 - Prob. 2E Ch. 7.1 - Prob. 3E Ch. 7.1 - Prob. 4E Ch. 7.1 - Prob. 5E Ch. 7.1 - Prob. 6E Ch. 7.1 - Prob. 7E Ch. 7.1 - Prob. 8E Ch. 7.1 - Prob. 9E Ch. 7.1 - Prob. 10E

Ch. 7.1 - Prob. 11E Ch. 7.1 - Prob. 12E Ch. 7.1 - Prob. 13E Ch. 7.1 - Prob. 14E Ch. 7.1 - Prob. 15E Ch. 7.1 - Prob. 16E Ch. 7.1 - Prob. 17E Ch. 7.1 - Prob. 18E Ch. 7.1 - Prob. 19E Ch. 7.1 - Prob. 20E Ch. 7.1 - Prob. 21E Ch. 7.1 - Prob. 22E Ch. 7.1 - Prob. 23E Ch. 7.1 - Prob. 24E Ch. 7.1 - Prob. 25E Ch. 7.1 - Prob. 26E Ch. 7.1 - Prob. 27E Ch. 7.1 - Prob. 28E Ch. 7.1 - Prob. 29E Ch. 7.1 - Prob. 30E Ch. 7.1 - Prob. 31E Ch. 7.1 - Prob. 32E Ch. 7.1 - Prob. 33E Ch. 7.1 - Prob. 34E Ch. 7.1 - Prob. 35E Ch. 7.1 - Prob. 36E Ch. 7.1 - Prob. 37E Ch. 7.1 - Prob. 38E Ch. 7.1 - Prob. 39E Ch. 7.1 - Prob. 40E Ch. 7.1 - Prob. 41E Ch. 7.1 - Prob. 42E Ch. 7.1 - Prob. 43E Ch. 7.1 - Prob. 44E Ch. 7.1 - Prob. 45E Ch. 7.1 - Prob. 46E Ch. 7.1 - Prob. 47E Ch. 7.1 - Prob. 48E Ch. 7.1 - Prob. 49E Ch. 7.1 - Prob. 50E Ch. 7.1 - Prob. 51E Ch. 7.1 - Prob. 52E Ch. 7.1 - Prob. 53E Ch. 7.1 - Prob. 54E Ch. 7.1 - Prob. 55E Ch. 7.1 - Prob. 56E Ch. 7.1 - Prob. 57E Ch. 7.1 - Prob. 58E Ch. 7.1 - Prob. 59E Ch. 7.1 - Prob. 60E Ch. 7.1 - 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