You own one call option contract on Dell Computer with an exercise price of $45 and a remaining maturity of three months. The current price of Dell is $50 per share and the risk-free rate of interest is 5 percent per year with continuous compounding. Dell does not pay dividends and does not expect to do so in the near future. Answer the following questions.

a. Prove that it would never be optimal to exercise your Dell call option contract now if you can sell the contract in the market.

b. What if you cant sell the option (for whatever reason) and you know (dont ask me how) that Dells stock price will be much lower in the future. Should you exercise the option now and take the profit or wait until the expiration date of the option contract? Provide a detailed and rigorous answer to this question.