word prob
He cannot simply plant as many trees as he can, since planting more trees will decrease the amount of fruit that each tree produces (the yield of each tree).
He has found that the per-tree yield can be described by the equation
Y = 1200 - 15 x.
Here Y is the yield per tree and x is the number of trees planted per acre.
For example, if there were 10 trees planted per acre, each tree would produce 1200 - 15 * 10 = 1050 peaches.
Find the number of trees per acre that should be planted in order to produce the maximum crop and the resulting total yield.
Number of trees per acre : trees per acre
Total yield : peaches per acre
Homework Answers
X = Trees per acre
Number of Peaches per tree = 1200 - 15X
So...
Number of peaches per acre = 1200 - 15X1200 - 15X
= 1200X - 15X2
We now need to max of this parabola. We can do this by finding the derivative and finding where it equals to zero.
(1200X -15X2) = 1200 - 30X
0 = 1200 - 30X Find X
X = 40
Numbers of trees per acre: 40 Trees
Peaches per acre :
Plug X= 40 back in the equation
(40)(1200 - 15(40)) = 24000 peaches
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