Question 1048446: The cost, in dollars, to produce x "I'd rather be a Sasquatch" T-Shirts is
C(x)=2x+26, x≥0 and the price-demand function, in dollars per shirt, is
p(x)= 30-2x, 0≤x≤15.
a)Find the profit function P(x).
b)Find the number of items which need to be sold in order to maximize profit.
c)Find the maximum profit.
d)Find the price to charge per item in order to maximize profit.
e)Find and interpret break-even points.
I came up with the following solutions, which are correct per the answer section:
a) P(x)= -2x²+28x-26
b) $7
c) Max profit: $72
d) price to charge for max. profit: $16
e) Cannot figure out. The given solutions per textbook are 1 and 13.
PLEASE HELP WITH E)!
THANK YOU!
Answer by ewatrrr(24785)   (Show Source):
You can put this solution on YOUR website! RE: TY, e) included
Profit(x) = R(x) - C(x) where R(x) = px = (30-2x)x
P(x) = (30x - 2x^2) -(2x+26)
P(x) = 30x - 2x^2 -2x-26)
And Yes
a) P(x) = -2x^2 + 28x - 26
completing the square:
P(x) = -2(x -7)^2 + 98(49*2) - 26 = -2(x -7)^2 + 72 Parabola opening downward
V = (7,72)
(b&c)x = 7 (# of items sold at max point) and P(x) = $72 (maximum profit)
d) price = 30- 2x, = 30-14 = $16
e) Calculate and interpret the break-even point
R(x) = C(x)
(30x - 2x^2)=(2x+26)
2x^2 -28x + 26 = 0
x^2 - 14x + 13 = 0
(x-13)(x-1) = 0
x = 1, 13
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