10. (The happy call) A New York firm is offering a new financial instrument called a "happy call" It has a payoff function at time 7 equal to max( 55, SK), where S is the price of a stock and K is a fixed strike price. You always get something with a happy call. Let P be the price of the stock at time = 0 and let C and C be the prices of ordinary calls with strike prices K and 2K, respectively. The fair price of the happy call is of the form C =P+BC+yC Find the constants

a, B, and y