Can you show a breakdown of how you solve this problem

Dayna's Doorstops, Inc. (DD) is a monopolist in the doorstop industry. Its cost is TC = 100 - 5Q + Q2 , and (inverse) demand is P = 55 - 2Q.

A. What price should DD set to maximize profits? What output does the firm produce? How much profit and consumer surplus does DD generate?

B. What would output be if DD acted like a perfect competitor and set MC = P? What profit and consumer surplus would then be generated?

C. What is the deadweight loss from monopoly power in part A?

[Hint: for each of D., E., and F., check whether the firm would be willing to supply the quantity demanded at the respective price. Remember that the firm will only supply if MCP. If MC>P, you need to compute the quantity that the firm would supply, i.e., where MC=P, and this may be smaller than quantity demand, so that there is a shortage.]

For the remainder suppose that DD acts as a profit-maximizing monopolist.

D. Suppose the government, concerned about the high price of doorstops, sets a maximum price at $27. How does this affect price, quantity, consumer surplus and DD's profits? What is the resulting deadweight loss?

E. Now suppose the government sets the maximum price at $23. How does this decision affect price, quantity, consumer surplus, DD's profit, and deadweight loss?

F. Finally, consider a maximum price of $12. What will this do to quantity, consumer surplus, profit and deadweight loss?