SOLUTION: Cali is selling candles at a stand in the mall. She currently sells the candles for $14 each. At this price, she sells 260 candles a week. She is considering raising the price of t

Question 427350: Cali is selling candles at a stand in the mall. She currently sells the candles for $14 each. At this price, she sells 260 candles a week. She is considering raising the price of the candles to make a greater profit. Her college statistics class determined that she will lose 10 sales for every one dollar increase in price. What would provide Cali with the most profit? What is her maximum weekly profit?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
She currently sells the candles for $14 each.
At this price, she sells 260 candles a week.
She is considering raising the price of the candles to make a greater profit.
Her college statistics class determined that she will lose 10 sales for every one dollar increase in price.
What would provide Cali with the most profit? What is her maximum weekly profit?
:
Let x = no. of dollar increase, and no. of candle sales decrease
:
f(x) = (260 - 10x) * (14 + x):
FOIL
f(x) = 3640 + 260x - 140x - 10x^2
:
f(x) = -10x^2 + 120x + 3640
:
Max revenue would be at the axis of symmetry: x = -b/(2a); a=-10, b=120
x =
x = 6 dollar increase, and 60 candle decrease
:
What is her maximum weekly profit?
(14+6) * (260 - 60) = $4000
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