Demand (q) for good X is a linear decreasing function of price: q = a - bp. A company sells good X and faces the following profit function: pi(q) = pq - vq - F. Assume that a = 10000 units, b = 800 units/$, v = $5/unit and F = $10,000. Required: Express profit as a function of price alone. (Write out the profit function with p as the only variable.) What would demand be if the company gave good X away for free? What is the profit maximizing price, p_max? At p_max how many units will be demanded and what will profit be? At what prices, p*_1 and p*_2 will the company break-even? What is the price elasticity of demand at p_max? At p*_1 and p*_2? Is demand for the good relatively elastic or inelastic at p_max, p*_1 and p*_2? At what price, p**, between [0, infinity] will the company begin to lose sales revenue if they charged a price higher than p**? Graph profit as a function of price (profit on vertical axis) and label p_max, pi(p_max), p*_1, p*_2 and p**