SOLUTION: Please help me solve this problem: A soft-drink vendor at a popular beach analyzes his sales records, and finds that if he sells x cans of soda pop in one day, his profit (in dolla

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Question 1034547: Please help me solve this problem: A soft-drink vendor at a popular beach analyzes his sales records, and finds that if he sells x cans of soda pop in one day, his profit (in dollars) is given by P(x) = -0.001x2+ 3x – 1800.
a. What is his maximum profit per day?
b. How many cans must be sold in order to obtain the maximum profit?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
When +P%28x%29+ is a maximum, the formula
for the x-value is: +x%5Bmax%5D+=+-b%2F%282a%29+
when the form of the equation is:
+P%28x%29+=+ax%5E2+%2B+b%2Ax+%2B+c+
+a+=+-.001+
+b+=+3+
+c+=+-1800+
+-b%2F%282a%29+=+-3%2F%282%2A%28-.001%29+%29+
+-b%2F%282a%29+=+3%2F.002+
+-b%2F%282a%29+=+1500+
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Plug this value back into equation to get +P%281500%29+
+P%281500%29+=+-.001%2A1500%5E2+%2B+3%2A1500+-+1800+
+P%281500%29+=+-2250+%2B+4500+-+1800+
+P%281500%29+=+450+
-------------------
(a)
His maximum profit/day is $450
(b)
He must sell 1500 cans/day to reach this profit
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Here's the plot:
+graph%28+400%2C+400%2C+-200%2C+2300%2C+-50%2C+600%2C+-.001x%5E2+%2B+3x+-+1800+%29+