At a price of $\$ 200$, a company will be able to sell 1,000 units of its product in a month. If the selling price is increased to $\$ 220$, the demand will fall to 950 units. It is also known that the product has a variable cost of $\$ 140$ per unit, and fixed costs will be $\$ 36,000$ per month.

Required:

(a) Find an equation for the demand function (that is, price as a function of quantity demanded)

(b) Write down the marginal revenue function

(c) Write down the marginal cost

(d) Find the quantity that maximises profit

(e) Calculate the optimum price

(f) What is the maximum profit?