SOLUTION: A student club is planning a fundraising carwash. Last year, they charged 100 per vehicle & washed 120 vehicles. If for every 20 increase in price, they know they will wash 5 fewer

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Question 1092291: A student club is planning a fundraising carwash. Last year, they charged 100 per vehicle & washed 120 vehicles. If for every 20 increase in price, they know they will wash 5 fewer vehicles. Determine the best price to charge for the car wash so that the proceeds is maximum.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+P+=+%28+100+%2B+20n+%29%2A%28+120+-+5n+%29+
+P+=+12000+%2B+2400n+-+500n+-+100n%5E2+
+P+=+-100n%5E2+%2B+1900n+%2B+12000+
The formula for the n-value of the vertex is
+n%5Bmax%5D+=+-b%2F%282a%29+
+n%5Bmax%5D+=+-1900+%2F+%282%2A%28-100%29%29+
+n%5Bmax%5D+=+9.5+
and, also
+P%5Bmax%5D+=+-100%2A9.5%5E2+%2B+1900%2A9.5+%2B+12000+
+P%5Bmax%5D+=+-100%2A90.25+%2B+18050+%2B+12000+
+P%5Bmax%5D+=+-9025+%2B+30050+
+P%5Bmax%5D+=+21025+
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The best price to charge is:
+100+%2B+20n+=+100+%2B+20%2A9.5+
+100+%2B+20n+=+290+
$290 per vehicle
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Here's the plot:
+graph%28+700%2C+400%2C+-2%2C+25%2C+-25%2C+250%2C+-x%5E2+%2B+19x+%2B+120+%29+
The P-values are all divided by +100+
Definitely try to get another opinion if needed