Based on market research, a film production company in Ectenia obtains the following information about the demand and production costs of its new DVD:

Demand: P=1000-10Q
Total Revenue: TR=1000Q-10QZ
Marginal Revenue: MR=1000-20Q
Marginal Cost: MC=100+10Q
Where Q indicates the number or copies sold and P is the price in Ectenian dollars.

a. Find the price and quantity that maximizes the companies profit.
b. Find the price and quantity that would maximize social welfare.
c. find out the deadweight loss from monopoly
d. Suppose, in additional to the costs above, the director of the film has to be paid. The company is considering four options:
i). A flat fee of 2,000 Ectenian dollars
ii). 50% of the profits
iii). 150 Ectenian dollars per unit sold
iv). 50% of the revenue

For each option, find out the profit-maximizing price and quantity. Which, if any, of these compensation schemes would alter the deadweight loss from monopoly? describe.