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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?

 Oct 8, 2021
 #2
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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                                              

 Oct 8, 2021

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