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Question 215071: I'm having trouble setting up this question, help would be appreciated:
Research has shown that if 100 pear 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 pears per tree. As a result, the annual revenue per free is reduced $0.70 for each additional tree planted. No matter how many trees are plated, the cost of maintaining each tree is $7.40 per year. How many pear trees should be planted to maximize the profit from the orchard for one year?
Let 'x' represent the amount of pear trees planted.
Profit = Revenue - Cost
Revenue = (90-0.7x)(100+x)
Cost = 7.40(100+x)
Profit = 9000+90x-70x-0.7x^2-740+7.4x
The function I work out is:
However I can't work it out correctly, can someone help me set this problem up?? Thanks in advance.
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! Research has shown that if 100 pear 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 pears per tree.
As a result, the annual revenue per tree is reduced $0.70 for each additional tree planted.
No matter how many trees are planted, the cost of maintaining each tree is $7.40 per year.
How many pear trees should be planted to maximize the profit from the orchard for one year?
:
Let 'x' represent the amount of pear trees planted.
Profit = Revenue - Cost
Revenue = (90-0.7x)(100+x)
Cost = 7.40(100+x)
Right here I think you made a mistake
Profit = 9000 + 90x - 70x - 0.7x^2 - 7.40(100 + x)
which is
Profit = 9000 + 90x - 70x - 0.7x^2 - 740 - 7.4x; (you had +7.4x}
Profit = 9000 + 20x - 0.7x^2 - 740 - 7.4x;
Profit = 9000 - 740 + 20x - 7.4x - 0.7x^2
:
So you would have
-0.7x^2 + 12.6x + 8260
:
A quadratic equation so we can find the axis of symmetry of x for max profit
x = -b/(2a)
in this equation a = -.7; b = 12.6.
x = 
x = 
x = 9 more trees, making it 109 trees for max profit
:
:
You certainly had the right idea, just a little sign error.
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