Which auction maximizes the sellers expected revenue- what

Question

Suppose there are n buyers participating in an auction, where the private values V₁, V₂,...,V_n are independent and identically distributed, with the cumulative distribution function

F_i(v_i) = 1/2 v_i + 1/2 (v_i)^2, v_i ∈ [0,1].

Answer the following questions:

(a) Which auction maximizes the seller's expected revenue?

(b) What is the seller's expected revenue in this auction? (To answer this, it suffices to write the formula for the seller's expected revenue, and specify the values of the variables. There is no need to compute the formula explicitly.)

(c) Is the seller's expected revenue monotonically increasing as the number of buyers in the auction increases? Justify your answer.