Date Mod P=R Key Concepts: E, where P is profit, R is revenue, and E is expenses. The vertex of a profit function lies on the axis of symmetry. The vertex of a profit function contains the maximum profit. Maximum profit can be found on the graph where the difference between the revenue and expense functions is the greatest. Guided Exercises FunFleece Incorporated manufactures fleece hats. It is considering making a new type of weatherproof fleece hat. The expense and revenue functions are E=-300p+ 150,000 and R = -300p2 + 29,000p. 1. Determine the profit function. P=R-E Substitute the expense function for E and the revenue function for R. P = (-300p2+29,000p) - (-300p + 150,000) P = P = The profit function is P = + 2. Use the equation from Exercise 1. Determine the maximum profit to the nearest cent. Determine the price that yields maximum profit. Find the maximum of the profit equation. Axis of symmetry = - b/2a Substitute the price, p, into the profit equation from Exercise 1. Axis of symmetry = - 2( P = D=