Problem 3: Producer Surplus Problem 3 Suppose you own a business that sells appliances. You plan to expand your business into a new region. Based on past market data, you know you can sell 400 units at $1500 each, or 200 units at $2300 each. Based on marginal costs, you approximate the following supply function: p = S(q) = 0.02q2 + 100 a. Using the information provided, determine the demand function, p = D(q). (Hint: it should be the equation of a line). b. Draw a rough sketch the supply and demand functions. In your sketch, include the location of the equilibrium point and the regions representing the producer and consumer surpluses. c. Find the equilibrium point using algebra. d. Determine producer surplus using calculus