$(20\%)$

Two$-$month European call options with strike prices of $$50,$$$60,$ and $$70$ cost $$12,$$$6,$

and $$4,$ respectively.

$($i$)$ What is the maximum gain when a butterfly spread is created from the call options?

$($ii$)$ What is the maximum loss when a butterfly spread is created from the call options?

$($iii$)$ For what two values of the stock price in three months does the holder of the

butterfly spread breakeven with a profit of zero?