The fruit tree yield per tree in an orchard containing 20 trees is 252 pounds per tree each year. due to crowding, the yield decreases by 3 pounds per tree for every additional tree planted. if you wish to maximize the total annual yield, what is the total number of trees that should be in the orchard?

Step-by-step explanation:

Let the number of fruit trees planted additionally be

Initially it is given that there are trees.

Number of trees after planting additional trees is

Let the yield due to each tree after planting additional trees be

Initially it is given that

Yield due to each tree after planting trees is

                                 =

To maximise yield,we take that value of for which

 =

So, and

So,32 additional trees has to be planted to maximise yield.

So,there should be 52 trees in total

step-by-step explanation:

first, eliminate the parenthesis:

3

x

+

2

−

4

x

second, group like terms:

3

x

−

4

x

+

2

third, combine like terms:

(

3

−

4

)

x

+

2

→

−

1

x

+

2

→

−

x

+

2