SOLUTION: the profit for a veggie dog vendor is given by this function: p(v)=-.004v^2+1.32v+200, where v is the number of veggie dogs sold per day. how many veggie dogs does she need tto sel

Algebra ->  Customizable Word Problem Solvers  -> Finance -> SOLUTION: the profit for a veggie dog vendor is given by this function: p(v)=-.004v^2+1.32v+200, where v is the number of veggie dogs sold per day. how many veggie dogs does she need tto sel      Log On

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Question 1042613: the profit for a veggie dog vendor is given by this function: p(v)=-.004v^2+1.32v+200, where v is the number of veggie dogs sold per day. how many veggie dogs does she need tto sell in a day to make a maximum profit
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
When the form of the equation is:
+f%28x%29+=+a%2Ax%5E2+%2B+b%2Ax+%2B+c+, then the
formula for the x-value of the vertex
( a peak in this case ) is:
+x%5Bmax%5D+=+-b%2F%282a%29+
----------------------
+p%28v%29+=+-.004v%5E2+%2B+1.32v+%2B+200+
+a+=+-.004+
+b+=+1.32+
----------------
+v%5Bmax%5D+=+-1.32+%2F+%28+2%2A%28-.004+%29%29+
+v%5Bmax%5D+=+1.32%2F.008+
+v%5Bmax%5D+=+165+
-----------------
She needs to sell 165 hot dogs/day to
maximize profit
------------------------------------
check:
Plug this value back into the equation to
get the maximum profit, +p%28v%29%5Bmax%5D+
----------------------------------
+p%28v%29%5Bmax%5D+=+-.004%2A165%5E2+%2B+1.32%2A165+%2B+200+
+p%28v%29%5Bmax%5D+=+-.004%2A27225+%2B+1.32%2A165+%2B+200+
+p%28v%29%5Bmax%5D+=+-108.9+%2B+217.8+%2B+200+
+p%28v%29%5Bmax%5D+=+108.9+%2B+200+
+p%28v%29%5Bmax%5D+=+308.9+
-------------------------
Here's the plot:
+graph%28+600%2C+400%2C+-60%2C+500%2C+-30%2C+350%2C+-.004x%5E2+%2B+1.32x+%2B+200+%29+