SOLUTION: Sales of a soft drink produces profits in accordance with: P(x)= -0.001x^2+3x-1800 per day, where P is profits in dollars and x is quantity of cans. What is the maximum profits per

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Question 684409: Sales of a soft drink produces profits in accordance with: P(x)= -0.001x^2+3x-1800 per day, where P is profits in dollars and x is quantity of cans. What is the maximum profits per day & how many cans must it sell to gain maximum profits??
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+P%28x%29=+-.001x%5E2%2B3x-1800+
The x-co-ordinate of the maximum is at +x%5Bmax%5D+=+-b%2F%282a%29+
+x%5Bmax%5D+=+-3%2F%282%2A%28-.001%29%29+
+x%5Bmax%5D+=+3%2F.002+
+x%5Bmax%5D+=+1500+
They must sell 1500 cans to maximize profit
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+P%28x%29=+-.001x%5E2%2B3x-1800+
+P%281500%29=+-.001%2A1500%5E2+%2B+3%2A1500+-+1800+
+P%281500%29=+-.001%2A2250000+%2B+4500+-+1800+
+P%281500%29=+-2250+%2B+4500+-+1800+
+P%281500%29+=+4500+-+4050+
+P%281500%29+=+450+
Their maximum profit per day is $450
check answer:
+P%28x%29=+-.001x%5E2%2B3x-1800+
+450+=+-.001%2A1500%5E2+%2B+3%2A1500+-+1800+
+450+=+-.001%2A2250000+%2B+4500+-+1800+
+450+=+-2250+%2B+4500+-+1800+
++4050+%2B+450+=+4500+
+4500+=+4500+
OK