Problem 6 (Complete bounds on call price). (10 pts) Consider the market with one stock and one bond. We know the initial value of the stock S0=50 and the continuous compounding interest rate r=1%. Also, we know the initial market price of a European call option with strike price K=30 and maturity time T=1 is C0E,30=20 and the initial market price of another European call option with strike price K=60 and the same maturity T=1 is C0E,60=10. Now, suppose you want to write and sell a European call option written on the same stock with strike price K=50 and the same maturity time T=1, find the best upper and lower bounds for the initial price of your European call option. (Round your answer to the nearest tenths) (Hint: Use the following inequolities: bounds on option prices, monotonicity on K, growth rate on K, convexity on K.)