SOLUTION: Pauline wants to sell stainless steel water bottles as a school fundraiser. She knows that she will maximze prophits and raise 1024 dollars if she sells the bottles for 28 dollars

Question 375890: Pauline wants to sell stainless steel water bottles as a school fundraiser. She knows that she will maximze prophits and raise 1024 dollars if she sells the bottles for 28 dollars each. she also knows that she will lose 4160 dollars if she sells the bottles for only 10 dollars each.
a) Write a quadratic relation to model her profit. P in dollars if she sells the bottles for x dollars each
b) What selling price will ensure that she breaks even
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
She knows that she will maximze prophits and raise 1024 dollars if she sells
the bottles for 28 dollars each.
she also knows that she will lose 4160 dollars if she sells the bottles for only 10 dollars each.
:
Find how many bottles are being sold. Let n = no. of bottles sold
28n = 1024
10n = -4160
-------------subtract
18n - 5184
n = 5184/18
n = 288 bottles
Find the profit made on each bottle
1084/288 = $3.76
find the cost of each bottle
28 - 3.76 = $24.24
:
a) Write a quadratic relation to model her profit.
P in dollars if she sells the bottles for x dollars each
:
P = 288(x - 24.24)
:
b) What selling price will ensure that she breaks even
288(x - 24.24) = 0
288x - 6981.12 = 0
288x = 6981.12
x =
x = $24.24, will break even (obviously)
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