x = price charged
30 - 3(x-10) = number sold
profit = revenue - cost
P(x) = x[30 - 3(x-10)] - 6[30 - 3(x-10)]
I'll leave it to you to simplify the algebra for the profit model.
I've attempted to figure out this problem for the last half hour. I made a chart and everything but still don't know how I'm supposed to model the function.
Here's the problem:
A community of bird watches makes and sells simple bird feeders. The materials for each feeder costs $6, and the society sells an average of 30 per week at a price of $10 each. The society has been considering raising the price, so it conducted a survey and found 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 be the price per feeder and P(x) be the profit)
P(x) = ???
B) What price should the society charge for each feeder to maximize profits?
C) What is the maximum weekly profit? (Round your answer to the nearest dollar)
Thanks in advance! My math teacher pretty much leaves us to our own resources so that's why I'm here. I greatly appreciate your help.