The Market Demand for the Output of a Public Utility $$Q D = 250 - 2 P$$

The market demand for the output of a public utility is:
$$Q D = 250 - 2 P$$ The firm's long-run average cost and long-run marginal cost functions are:
$$L A C = 50 - 0.125 Q \text { and } L M C = 35 - 0.10 Q$$ (i)What price and quantity combination would result if the firm was not regulated? How much profit would the firm earn?
(ii)What price and quantity combination would result if the firm was regulated at a price that resulted in an economic profit of zero?
(iii)What price and quantity combination would result if the firm was regulated at a price that resulted in the socially optimal level of output? How much profit would the firm earn?