Produce a graph comparing a calls intrinsic value [defined as max(S-X,0)] and its Black-Scholes price. Stock prices to produce respective intrinsic values should start at 36 and end at 68 (units of 2). From this graph, provide an explanation of why it is never optimal to exercise early on a call priced by the Black-Scholes. Use the inputs above.

Black-Scholes option pricing formula \begin{tabular}{|l|r|l|l|} \hline S & 50 & current stock price \\ \hline X & 50 & exercise price \\ \hline r & 10.00% & risk-free rate of interest \\ \hlineT & 0.5 & time to maturity of option (in years) \\ \hline Sigma & 25% & stock volatility \\ \hline d1 & & \\ \hline d2 & & & \\ \hline & & & \\ \hlineN(d1) & & & \\ \hlineN(d2) & & & \\ \hline & & & \\ \hline call price & & & \\ \hline put price & & & \\ \hline \end{tabular} \begin{tabular}{|r|c|c|c|c|} \hline Stock & B-S & Intrinsic & \\ \hline Price & Value & Value & & \\ \hline & & & & \\ \hline 36 & & & & \\ \hline 38 & & & & \\ \hline 40 & & & & \\ \hline 42 & & & & \\ \hline 44 & & & & \\ \hline 46 & & & & \\ \hline 48 & & & & \\ \hline 50 & & & & \\ \hline 52 & & & & \\ \hline 54 & & & & \\ \hline 56 & & & & \\ \hline 58 & & & & \\ \hline 60 & & & & \\ \hline 62 & & & & \\ \hline 64 & & & & \\ \hline 66 & & & & \\ \hline 68 & & & \\ \hline \end{tabular}