# The number of trees should be planted per acre to obtain the maximum yield of apples.

BuyFind

### Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071
BuyFind

### Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

#### Solutions

Chapter 3.1, Problem 69E
To determine

Expert Solution

## Answer to Problem 69E

The number of trees should be planted per acre to obtain the maximum yield of apples is 50trees/acre .

### Explanation of Solution

Given:

The number of apples produced per acre is given by the function A(n)=n(9009n) , where n is the number of trees per acre.

Calculation:

The function of the number of apples produced per acre is given by

A(n)=n(9009n)=900n9n2=9n2+900n (1)

The standard form of function,

f(n)=an2+bn+c (2)

The maximum or minimum value of the function occurs at,

n=b2a (3)

If a>0 , then the minimum value is f(b2a) .

If a<0 , then the maximum value is f(b2a) .

From the equation (1) and (2),

a=9b=900

Substitute 9 for a and 900 for b in the equation (3),

n=9002×9=90018=50

The number of trees per acre is 50 .

The function has maximum value,

a=9<0 .

Thus, the number of trees should be planted per acre to obtain the maximum yield of apples is 50trees/acre .

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