This is an example of an optimisation problem using linear programming. Have a look at this and see if it makes sense:
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Please Help I am completely confused on how to do this. Thanks
REVENUE : An apple orchard produces annual revenue of $60 per tree when planted with 100 trees. Because of overcrowding, the annual revenue per tree is reduced by $0.50 for each additional tree planted.
Assuming , write an equation for the revenue produced by trees:
How many trees should be planted to maximize the revenue from the orchard?
Now suppose that the cost of maintaining each tree is $5 per year.
Write the profit function in terms of :
How many trees should be planted to maximize the profit from the orchard?
Hello, boondocksaint202!
For every tree over 100, the revenue per tree is reduced byAn apple orchard produces annual revenue of $60 per tree when planted with 100 trees.
Because of overcrowding, the annual revenue per tree is reduced by $0.50
for each additional tree planted.
(a) Assuming , write an equation for the revenue produced by trees.
The overage is .
This reduced the revenue to: . dollars per tree.
The Revenue is: .[no. of trees ] x [revenue per tree]
. .
The Revenue function is: .(b) How many trees should be planted to maximize the revenue from the orchard?
This is a down-opening parabola; its maximum is at its vertex.
. . The vertex is at: .
We have: .
Hence: .
Therefore, 110 trees should be planted for maximum revenue.
For trees, the cost is: . dollars.(c) Suppose that the cost of maintaining each tree is $5 per year.
. . Write the profit function in terms of
. .
. . .
The profit function is: .(d) How many trees should be planted to maximize the profit from the orchard?
This is a down-opening parabola ... with its maximum at its vertex.
The vertex is at: .
Therefore, 105 trees should be planted for maximum profit.