Question $3(20$ points$)$ A search engine can sell two ad slots. Slot A has a clickthrough rate of $0\mathrm{.}03$ and slot B has a clickthrough rate of $0\mathrm{.}04.$ There are three advertisers who are interested in buying these slots. The value obtained per click is $10$ for advertiser X$,40$ for advertiser Y and $30$ for advertiser Z$.($a$)$ Suppose that the search engine runs the VCG procedure to allocate slots. What are the slot assignments and the prices paid by the advertisers? Explain. $(10$ points$)($b$)$ The search engine can create a third ad slot, C$,$ with a clickthrough rate of $0\mathrm{.}02.$ What will be the assignment of slots and what prices will the advertisers pay if the search engine creates slot C and again uses the VCG procedure to allocate slots? Do you think the search engine should create slot C$?(10$ points$)$