The current share price of Gator Corp. is $$40.$ The following three call options are available

on the stock:

$1.$ The price of a $$35-$strike $1-$year European call option is $$9\mathrm{.}12.$

$2.$ The price of a $$40-$strike $1-$year European call option is $$6\mathrm{.}22.$

$3.$ The price of a $$45-$strike $1-$year European call option is $$4\mathrm{.}08.$

The annual effective risk$-$free interest rate is $8\%.$ Let $$S$$ be the stock price of the Gator Corp. one year from now. Assuming you are only taking long positions in these call options due to your limited risk appetite. Determine the range for $$S$$ such that the $45-$strike call produces a higher profit than the $40-$strike call, but a lower profit than the $35-$strike call.