SOLUTION: A specialty entertainment store find that if it sells x life-size animatronic Bryce Harper statues per month, its profit (In dollars) will be P(x)=-60x^2+1800x-7500. A. Find a

Algebra ->  Finance -> SOLUTION: A specialty entertainment store find that if it sells x life-size animatronic Bryce Harper statues per month, its profit (In dollars) will be P(x)=-60x^2+1800x-7500. A. Find a      Log On


   



Question 1139816: A specialty entertainment store find that if it sells x life-size animatronic Bryce Harper statues per month, its profit (In dollars) will be P(x)=-60x^2+1800x-7500.
A. Find any break even points.
B. Find the number of items that need to be produced and sold in order to maximize the profit.
C. Find the maximum profit.

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
At break-even point, +P%28x%29+=+0+
+-60x%5E2+%2B+1800x+-+7500+=+0+
+-x%5E2+%2B+30x+-+125+=+0+
+%28+-x+%2B+25+%29%2A%28+x+-+5+%29+=+0+ ( by looking at it )
+x+=+25+
+x+=+5+
5 or 25 statues/mo give zero profit ( break even )
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The x-value of +P%5Bmax%5D+ is:
+P%5Bmax%5D+=+-b%2F%282a%29+
+P%5Bmax%5D+=+-1800%2F%282%2A%28-60%29%29+
+P%5Bmax%5D+=+1800%2F120+
+P%5Bmax%5D+=+15+
15 item/mo will maximize profit
-----------------------------------------
+P%2815%29+=+-60%2A15%5E2+%2B+1800%2A15+-+7500+
+P%5Bmax%5D+=+-60%2A225+%2B+27000+-+7500+
+P%5Bmax%5D+=+-13500+%2B+27000+-+7500+
+P%5Bmax%5D+=+6000+
$6000 is max profit
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Here's the plot:
+graph%28+400%2C+400%2C+-3%2C+30%2C+-700%2C+7000%2C+-60x%5E2+%2B+1800x+-+7500+%29+