The profit function is P(x) = (p - v)*x - f.
How the profit function is found:
The profit function P(x) equals the total revenue minus the total cost.
Let the price per unit of cookie = p
Let the quantity sold (number of cookies) = x
Let the variable cost per unit = v
Let the fixed cost = f
The total revenue R(x) = the price per unit times the quantity sold, or R(x) = p*x.
The total cost C(x) = the total variable cost plus the fixed cost, or C(x) = v*x + f.
The profit function P(x) = the total revenue minus the total cost, or P(x) = R(x) - C(x).
Substituting the expressions for R(x) and C(x) into this equation:
P(x) = px - (vx + f) = (p - v)*x - f
Therefore, the profit function P(x) = (p - v)*x - f, where:
(p - v) = the price per unit minus the variable cost per unit
f = the fixed cost.
Complete Question:
Find the profit function P(x) where x represents the number of cookies sold. Hint: Profit = Total Revenue - Total Cost.
Total Revenue = Price per unit x quantity sold.
Total Cost = Total variable cost + fixed cost.