You have decided to speculate in the options market but are a conservative, risk$-$averse person. Therefore, you use a CALL and a PUT options to limit your earnings or losses.

The stock you have selected to invest in today's price is $$50$ per share.

You buy a CALL option to buy $1000$ shares at $$47,$ due in three months. Option cost $$400.$

You buy a PUT option to sell $1000$ shares at $$67,$ due in three months. Option cost $$500.$

The market is turbulent, and the company's beta is $1\mathrm{.}75,$ so the probability of exercising both options is high.

a$.$ What is the maximum profit you may get from this operation, exercising both options?

b$.$ What would be your losses if$,$ after exercising the CALL option, the price continues dropping until $$30?$

c$.$ What will be your losses if the prices just move in the rank of $$48$ to $$55?$