The Market Demand for the Output of a Public Utility

The market demand for the output of a public utility is: QD = 250 - 2P
The firm's long-run average cost and long-run marginal cost functions are:
LAC = 50 - 0.125Q and LMC = 35 - 0.10Q
What price and quantity combination would result if the firm was not regulated?
What profits would the firm earn?
What price and quantity should the regulators set in order to make the profits of the public utility firm equal zero?
The firm's long-run average cost and long-run marginal cost functions are:
LAC = 50 - 0.125Q and LMC = 35 - 0.10Q
(i)(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?