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

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons -> 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      Log On


   



Question 904079: 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 josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+A%28n%29+=+%28+600+%2B+n+%29%2A%28+10+-+.01n+%29+
+A%28n%29+=+6000+%2B+10n+-+6n+-+.01n%5E2+
+A%28n%29+=+-.01n%5E2+%2B+4n+%2B+6000+
--------------------------------
This equation is in the form:
+a%2Ax%5E2+%2B+b%2Ax+%2B+c+
The vertex ( peak ) isd at:
+-b%2F%282a%29+=+-4%2F%282%2A%28-.01%29%29+
+-b%2F%282a%29+=+4%2F.02+
+-b%2F%282a%29+=+200+
200 vines will maximize production
check:
+A%28199%29+=+%28+600+%2B+199+%29%2A%28+10+-+1.99+%29+
+A%28199%29+=+799%2A8.01+
+A%28199%29+=+6399.99+
---------------------
+A%28201%29+=+%28+600+%2B+201+%29%2A%28+10+-+2.01+%29+
+A%28201%29+=+801%2A7.99+%29+
+A%28201%29+=+6399.99+
---------------------
+A%28200%29+=++%28+600+%2B+200+%29%2A%28+10+-+2+%29+
+A%28200%29+=+800%2A8+
+A%28200%29+=+6400+
OK