The seller has one item to sell. The seller has zero value for the item. There are two bidders whose values are drawn from F~U [0, 20] and F2 ~ U [10, 30]. (a) Find an optimal mechanism with bidder 1 only (i.e., one bidder) and the expected revenue. (5) (b) Find an optimal mechanism with bidder 2 only and the expected revenue. (10) (c) Find an optimal reserve price for the second-price auction (i.e., there exists only one reserve price) with bidders 1 and 2, and calculate the expected revenue. (10) (d) Find an optimal mechanism. Clearly show allocation and payment rules with an allocation diagram (20) (e) Calculate the expected revenue of the optimal mechanism in two ways. (10) i. marginal revenue integration (10) ii. payment integration