SOLUTION: There is one homework question I am stuck on and cannot understand what I am doing wrong. We are worknig on graph shifts. The question is, At a certain vineyard it is found that e

Click here to see ALL problems on Graphs

Question 617719: There is one homework question I am stuck on and cannot understand what I am doing wrong. We are worknig on graph shifts. The question is,
At a certain vineyard it is found that each grape vine produces about 10 pounds of grapes in a season when about 800 vines are planted per acre. For each additional vine that is planted, the production of each vine decreases by about 1 percent. So the number of pounds of grapes produced per acre is modeled byA(n)=(800+n)(10-0.01n) where n is the number of additional vines planted Find the number of vines that should be planted to maximize grape production.
I have come up with A(n)= -0.01(n+100)^2+8100 and put in the answer of 100, 8100, 800 and many others and nothing is right. I don't understand what I am doing wrong.
Found 2 solutions by solver91311, Theo:
Answer by solver91311(24713) (Show Source):
You can put this solution on YOUR website!

Not sure how you got to

But it is wrong.

Start with

And FOIL it:

Collect terms then go to standard quadratic form:

Note: If you multiply yours out and collect terms you are only off by the sign on the first degree term, but it is nevertheless incorrect.

Note that this is a polynomial function of the form the graph of which is a parabola. Since it has a negative lead coefficient, the parabola opens downward. Therefore, the vertex of the parabola is the maximum of the function. Recall that the -coordinate of the vertex of is given by

So calculate to find the number of vines in excess of 800 that should be planted to maximize the yield. Don't forget to add the answer to 800 to get the answer to the question posed by the problem.

John

My calculator said it, I believe it, that settles it

Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
your equation is:
a(n) = (800 + n) * (10 - .01n)
that doesn't look right.
let's see how it works.
if you don't plan an extra vine, then you will get:
a(0) = (800) * (10) which would equal 8000 pounds per acre per season.
if you add 1 vine to the acre, then your production is:
a(1) = (801) * (10 - .01) which would then be equal to:
a(1) = 801 * 9.99 which would be equal to 8001.99
1 percent of 10 is equal to .01 * 10 which is equal to .1
if you subtract .1 from 10, you get 9.9.
your problem appears to be in your factor.
the equation should be:
a(n) = (800 + n) * (10 - .01*n*10) which would then be equal to:
a(n) = (800 + n) * (10 - .1*n)
that's where i think you went wrong.
let's see if that straightens it out.
a(0) = 800 * 10 = 8000 so that's ok.
a(10) = (800 + 10) * (10 - .1*10) which is equal to:
a(10) = (810) * (9) which is equal to 7290
let's see if this makes sense.
you add 10 vines to the acre and your yield decreases by 1 percent for each additional vine that's planted.
if so, then your yield per vine should have decreased from 10 pounds to 9 pounds.
that gets you 9 * 810 = 7290 pounds.
i think the equation is now correct.
check it out and let me know how you did.