Final answer:
The profit function for Charlie's weekly profit, when charging x dollars per birdhouse, is P(x) = 87x - 4x^2, where P(x) represents the profit and x represents the price per birdhouse.
Step-by-step explanation:
The question is asking to find a function for Charlie's weekly profit based on the charge x dollars per birdhouse and the fact that he can sell 87-4x birdhouses per week. To determine the profit function, we multiply the price per birdhouse x with the number of birdhouses sold 87-4x. This results in the profit function P(x) = x(87-4x). Expanding this, we get P(x) = 87x - 4x2, which is a quadratic function representing Charlie's profit.