Pls help with this problem! Thanks so much!

Question 2 (Non-Linear Pricing) A monopolist faces two types of consumers. The inverse demand function of each type-1 consumer is P = 100-20, while the inverse demand function of each type-2 consumer is: P = 80 - Q. The firm's cost function is given by: C(Q) = 200 + 100. Suppose first that the firm is able to tell whether a consumer is of type-1 or type-2 (e-g. by checking some form of ID). Suppose also that the firm uses a two-part tariff with each type. (a) Calculate the fixed fee and the price per unit for each type of consumers. {Hint: Draw diagrams to help you work through the problems.} Suppose now that the firm cannot tell whether a consumer is of type-1 or type-2. Therefore, suppose that the firm decides to offer the following packages: PACKAGE 1: 50 units packaged together for a total price of $2,500 PACKAGE 2: 40 units packaged together for a total price of $2,200 (b) For each package and each consumer-type, calculate willingness-to-pay (area under the respective demand curve) and associated consumer surplus (given price of each package). (c) Comparing the consumer surplus enjoyed by each consumer-type for each package, decide which package will be preferred by which consumer-type. (d) Assuming that there are 100 consumers of type-1 and 50 consumers of type-2, calculate the monopolist's profits