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October 25, 2014

October 25, 2014

Posted by **Q** on Tuesday, March 25, 2014 at 8:09pm.

I mostly need help getting an equation and defining a variable

- Calculus -
**Steve**, Tuesday, March 25, 2014 at 8:16pmthe number of apples is yield/tree * # trees.

With x trees, yield per tree is 200 - 5(x-50) for x > 50

So, total crop is

c(x) = x(200-5(x-50)) = x(450-5x) = 450x - 5x^2

c'(x) = 450-10x

c' = 0 at x=45

So, the max yield is achieved with 45 trees

- Calculus -
**bobpursley**, Tuesday, March 25, 2014 at 8:28pmnumber apples=average*number trees

let x be the nubmer of trees 50<x<inf

number apples=(200-(x-50)*5)(x) where x is the number of trees, 50<x<infinity

N=200x-5x^2 +250x

dN/dx=0=200-10x+250

10x=450

x=45

but x>50, so look at optimal

check x=50 N=50*200=10000 apples

check x=51 N=(51)(195)=9945

so indeed, the optimal is 50.

- Calculus -
**bobpursley**, Tuesday, March 25, 2014 at 8:29pmnow if you are allowed to remove trees, and for each tree removed, the average goes up by 5, then the optimal is to remove five trees.

- Calculus - good catch bob -
**Steve**, Tuesday, March 25, 2014 at 8:35pmDang - forgot the restriction on the domain.

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