The annual yield per lemon tree is fairly constant at 320 pounds when the number of trees per acre is 50 or fewer. For each additional tree over 50, the annual yield per tree for all trees on the acre decreases by 4 pounds due to overplanting. Find the number of trees that should be planted on an acre to produce maximum yield. How many pounds are produced?:confused:

Yes and what do you think ?

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Yes, please do some thinking of your own, Otherwise if we just give you the answer you probably won't understand anyway!

You need to engage with it to learn!

I'd be happy to help you if you have a bit of a go at it first :)

I already started to try.

I started with 50x+320y=P

I just don't know how to fit the decrease by 4 in.
I know that I have to get one variable, but I am kind of stuck. I was looking for a push in the right direction. Sorry.

Well Ask for a push and a push you shall get!

You have x trees producing 320 pounds each

P = 320x

Now, for each tree above 50, we lose 4*number of trees pounds

P = 320x - 4x(x - 50)

P = 320x - 4x^2 + 200x

P = 520x - 4x^2

You need to find when this is a maximum. I would recommend differentiating, setting dP/dx to 0 and solving for x

Is this in line with what your course is asking for? Or have I missed something?

I don't know how to do this particular sum with a quadratic. I don't think you are on the right lines with 50x+320y=P.

A simple way might be to do a sum, starting with 50Trees x 320lbs = Y, then do the same sum for 51 trees (remember that your crop is now 4lbs lighter per tree), so 51Trees x 316lbs = Y2. Now carry on adding trees and subtracting 4lbs for every tree added.

This will give you the answers, but how to solve with quadratic??

We have been doing these types of problems with two variables so I figured it had to have two. This is sort of a challenge problem that I have brought upon myself from the text book. Its not homework. I just wanted to see if I could figure it out. I have to maximize the yield.

I am just really confused because I factored the equation given below in one of the answers and I ended up with:

P=4x(130-x)

So then I just set them both equal to zero. I ended up with x=0 and x=130.

It doesn't make sense for each acre... or would I divide the 130 by 50?