A community bird-watching society makes and sells simple bird feeders to raise money for its conservation activities. The materials for each feeder cost $4, and the society sells an average of $24 per week at a price of $8 each. The society has been considering raising the price, so it conducts a survey and finds that for every dollar increase, it loses 3 sales per week.
(a) Find a function that models weekly profit in terms of price per feeder. (Let x represent the price per feeder and P represent the profit.)
(b) What price should the society charge for each feeder to maximize profits?
(c) What is the maximum weekly profit?
+36916 The number of units sold is dependent on the price
starts at 24 with price 8
as price rises by 1 units goes down by 3
units sold then becomes (24 - 3(x-8) ) = 48 - 3x
PROFIT is number of units sold * price - units sold * cost
(48-3x) * x - (48-3x) * 4 <=====simplify this
-3x^2 + 48x -192 + 12x
a) PROFIT = -3x^2 + 60x - 192
b) Max occurs at - b/2a = -60 / (-3*2) = 10 dollars price
c ) -3(10^2) + 60(10) - 192 = 108 dollars profit
