SOLUTION: Jessica sells T-shirts from her small kiosk in the shopping mall. On average, she sells 30 T-shirts per day at a price of $19.00 each. She estimates that she will sell 3 additiona

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Question 1014285: Jessica sells T-shirts from her small kiosk in the shopping mall. On average, she sells 30 T-shirts per day at a price of $19.00 each. She estimates that she will sell 3 additional shirts each day for every $1 reduction in the price per T-shirt.
Find a quadratic function modeling Jessica's daily revenue as related to reduction in price and the range of prices which would allow her to maintain or increase her current revenue.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +n+ = number of $1 increases in price
Let +R+ = daily revenue
+R+=+%28+30+%2B+3n+%29%2A%28+19+-+1%2An+%29+
+R+=+570+%2B+57n+-+30n+-+3n%5E2+
+R+=+-3n%5E2+%2B+27n+%2B+570+
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Note that if there are no reductions in price ( +n=0+ )
Then +R+=+570+ which is +R+=+30%2A19+
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What is the other value of +n+ that gives me +R+=+570+ ?
+R+=+-3n%5E2+%2B+27n+%2B+570+
570+=+-3n%5E2+%2B+27n+%2B+570+
+-3n%5E2+%2B+27n+=+0+
+n%2A%28+-3n+%2B+27+%29+=+0+
+-3n+%2B+27+=+0+
+3n+=+27+
+n+=+9+
Her revenue will be equal to or greater than $570 if the
$1 increases are between +0+ and +9+
That converts to price ranges of:
+19+-+1%2A0+=+19+ dollars/shirt
to
+19+-+1%2A9+=+10+ dollars/shirt
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Here's a plot of +R+ and n+
and +R+=+570+
+graph%28+400%2C+400%2C+-2%2C+12%2C+-50%2C+700%2C+-3x%5E2+%2B+27x+%2B+570%2C+570+%29+