A monopolist faces an inverse demand given by P = 1020 IDQ where P is the price of of the good they sell and Q represents the quantity produced and sold at the market price P. The monopolist's cost function is given by C (Q) = 10, 000 + EUQ where Q is the quantity produced and C represents the cost in dollars. a) Find the optimal price and quantity that the monopolist would choose under the assumption that their goal is to maximize prots. Show all of the steps required to arrive at the solution.1 b) Compute the prots of this monopolist. Show all of the steps required to arrive at the solution. c) - in a diagram with the market demand identify the deadweight loss (DWL) arising from this monopoly (DWL shape depends on demand and cost functions so make sure your sketch resemble the shapes of the particular cost and demand mctions 1n this problem) and then compute this amount. Hint: the size of a DWL is typically the area of some "triangle". Area of a triangle is just base*height. '.' and 9.4 in the textbook. (1) ' ' Now assume that the govermnent imposes a taxfunit of $100. Find (and show all of the steps required) the optimal price and quantity in the presence of this tax. Does the monopolist pass the whole: tax to consumers? Hint: compare the prices consumers would pa}.r without a tax, versus the new price the monopolist charges if there is a tax