SOLUTION: #1)Research for a given orchard 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 gen

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Question 257360: #1)Research for a given orchard 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 by $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 1 year?
#2) The sum of two numbe is 30 and their product is a maximum. Find the two numbers.
Answer by ankor@dixie-net.com(22740) (Show Source):
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#1)Research for a given orchard 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 by $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 1 year?
:
Let x = number of trees added, also the number of 70 cent reductions
:
Profit = (100 + x)*(90 - .70x) - 7.40(100 + x)
FOIL
P = 9000 - 70x + 90x - .70x^2 - 740 - 7.4x
:
P = 9000 + 20x - .70x^2 - 740 - 7.4x
Combine like terms
p = -.70x^2 + 20x - 7.4x + 9000 - 740
:
p = -.70x^2 + 12.6x + 8260
:
Find the axis of symmetry
x = ; where: a=-.7, b=12.6
x =
x =
x = +9 trees to be added
:
Max profit when 109 trees are planted $8,316.70
:
:
#2) The sum of two numbers is 30 and their product is a maximum. Find the two numbers.
:
that would be 15 + 15, 15^2 = 225
think of it like this; the max area (product of Length and width) is a square