The premiums for the call and put options with $1-$year to expiration for a stock are

given below.

The effective annual interest rate is $3\%.$ Construct an asymmetric butterfly spread position with three strike prices $50,59,$ and $65$ by using calls.

$($a$)$ Determine how many calls that you need to sell and buy respectively for the asymmetric butterfly spread position. Calculate the profit of the asymmetric butterfly spread position.

$($b$)$ When ST $=59,$ what the profit is$?$ Draw the graph of the profit.