SOLUTION: A store sells about 80 sweaters per month at a price of $ 30. For each $ 1 decrease in price, the store sells 5 more sweaters per month. Write a function that models this situation

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: A store sells about 80 sweaters per month at a price of $ 30. For each $ 1 decrease in price, the store sells 5 more sweaters per month. Write a function that models this situation      Log On


   

Question 1156061: A store sells about 80 sweaters per month at a price of $ 30. For each $ 1 decrease in price, the store sells 5 more sweaters per month. Write a function that models this situation. Tell how the store can maximize monthly revenue.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +R+ = monthly revenue
Let +n+ = number of $1 decreases in price
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+R+=+%28+30+-+1%2An+%29%2A%28+80+%2B+5n+%29+
+R+=+2400+-+80n+%2B+150n+-+5n%5E2+
+R+=+-5n%5E2+%2B+70n+%2B+2400+
The n-value of the peak is at:
+n%5Bmax%5D+=+-b%2F%282a%29+
+n%5Bmax%5D+=+-70%2F%28+2%2A%28-5%29%29+
+n%5Bmax%5D+=+7+
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If the store lowers the price by $7, the
monthly revenue will be maximum
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Here's the plot of +R+ and +n+:
+graph%28+500%2C+500%2C+-2%2C+20%2C+-300%2C+3000%2C+-5x%5E2+%2B+70x+%2B+2400+%29+
The maximum revenue is:
+R%5Bmax%5D+=+%28+30+-+1%2A7+%29%2A%28+80+%2B+5%2A7+%29+
+R%5Bmax%5D+=+23%2A115+
+R%5Bmax%5D+=+2645+
$2,645