Consider a manufacturer that sells his product to a dealer who resells it to final consumers. The market demand is given by P = 100 - Q. The manufacturer's constant marginal cost is $20 and the dealer's constant marginal cost is $10. The dealer's alternative profit (i.e., his profit if he does not operate in the market) is 0. The manufacturer offers the dealer a contract (w,T) where w is the wholesale price per unit and T is the lump sum that the dealer will pay to the manufacturer. a. What is the contract (w,T) that maximizes the manufacturer's profit?