In the Long-Run Equilibrium of a Competitive Market,the Market Supply

In the long-run equilibrium of a competitive market,the market supply and demand are:
Supply: P = 30 + 0.50Q
Demand: P = 100 - 1.5Q,
where P is dollars per unit and Q is rate of production and sales in hundreds of units per day.A typical firm in this market has a marginal cost of production expressed as:
MC = 3.0 + 15q.
a.Determine the market equilibrium rate of sales and price.
b.Determine the rate of sales by the typical firm.
c.Determine the economic rent that the typical firm enjoys.(Hint: Note that the marginal cost function is linear.)
d.If an output tax is imposed on ONE firm's output such that the ONE firm has a new marginal cost (including the tax)of: MC_t = 5 + 15q,what will the firm's new rate of production be after the tax is imposed? How does this new production rate compare with the pre-tax rate? Is it as expected? Explain.Would the effect have been the same if the tax had been imposed on all firms equally? Explain.