SOLUTION: At a certain vineyard it is found that each grape vine produces about 10 pounds of grapes in a season when about 600 vines are planted per acre. For each additional vine that is pl
Question 991261: At a certain vineyard it is found that each grape vine produces about 10 pounds of grapes in a season when about 600 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 by
A(n) = (600 + 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. Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website! At a certain vineyard it is found that each grape vine produces about 10 pounds of grapes in a season when about 600 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 by
A(n) = (600 + 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.
:
A(n) = (600 + n)(10 − 0.01n)
FOIL
A(n) = 6000 - 6n + 10n - .01n^2
A quadratic equation
y = -.01n^2 + 4n + 6000
The axis of symmetry will give us the maximum x = -b/(2a)
In this equation x = n; b = 4;
n =
n = 200 more vines, a total of 800 vines for max grape production
