SOLUTION: Mrs. Maths research has shown that if 100 apple trees are planted then the annual revenue is $90 per tree. If more trees are planted they have less room to grow and generate fewer

Question 866958: Mrs. Maths research has shown that if 100 apple trees are planted then the annual revenue is $90 per tree. If more trees are planted they have less room to grow and generate fewer apples per tree. As a result the annual revenue per tree is reduced by $0.70 for each additional tree planted. How many trees should be planted to maximize the revenue? Round your answer appropriately
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
If 100 apple trees are planted then the annual revenue is $90 per tree.
If more trees are planted they have less room to grow and generate fewer apples per tree.
As a result the annual revenue per tree is reduced by $0.70 for each additional tree planted.
How many trees should be planted to maximize the revenue?
:
Let x = no. of trees over 100
Let y = total revenue from the trees
:
y = (100+x)*(90-.70x)
FOIL
y = 9000 - 70x + 90x - .70x^2
A quadratic equation
y = -.7x^2 + 20x + 9000
At the axis of symmetry, x gives max revenue
x =
x = 14
We can say at 114 trees, we will have max revenue

RELATED QUESTIONS
#1)Research for a given orchard has shown that, if 100 pear trees are planted,then the... (answered by ankor@dixie-net.com)

Researach for a given orchard has shown that, if 100 pear trees are planted, then the... (answered by ankor@dixie-net.com)

I'm having trouble setting up this question, help would be appreciated: Research has... (answered by ankor@dixie-net.com)

If 100 pear trees are planted, then the annual revenue is $90 per tree. If more trees are (answered by josmiceli)

In a 6 acre apple orchard, it is decided to plant 20 or more trees per acre. If 20 trees... (answered by Theo)

There are 90 apple trees in an orchard. Each tree produces 1500 apples. There is a... (answered by Boreal)

The owner of the local apple orchard estimates that if 24 trees are planted per acre,... (answered by ikleyn,Theo)

Each orange tree grown in California produces 630 oranges per year if not more than 20... (answered by Boreal,ikleyn)

A fruit farmer planted a + 3 apple trees in each of a rows. If another row containing the (answered by edjones)