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Bird Feeders For Sale
math question precalculus?
A community bird-watching society makes and sells simple bird feeders to raise money for its conservation activities. The materials for each feeder cost $6, and they sell an average of 20 per week at a price of $10 each. They have been considering raising the price, so they conduct a survey and find that for every dollar increase they lose 2 sales per week.
(a). Find a function that models weekly profit in terms of price per feeder.
(b). What price should the society charge for each feeder to maximize profits? Whats the maximum profit?
a)
(p - 10)/(x - 20) = 1/-2
p - 10 = -x/2 + 10
p = -x/2 + 20
revenue r = px
r = -x^2/2 + 20x
profit f = r - c
c = 6x
f = -x^2/2 + 20x - 6x
f = -x^2/2 + 14x
b)
df/dx = -x + 14 = 0
x = 14 feeders
they should sell 14 feeders for maximum profit
the price p for maximum profit is
p = -14/2 + 20
p = $13
the maximum profit f is
f = -14^2/2 + 14*14
f = $98
Ferris Wheel Bird Feeder
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