The community bird-watching society creates and sells simple bird feeders to increase money for the conservation activities. Materials for every feeder cost $3, and society sells the average of 32 per week at the price of $7 each. Society has been considering raising price, so it performs the survey and finds that for every dollar increase, it loses 2 sales per week.
(a) Determine the function which models weekly profit in terms of price per feeder. Consider x be price per feeder and P(x) be profit.
(b) What price must society charge for every feeder to maximize profits? Find the maximum weekly profit?