Please Solve :

A six$-$month European call option on a GlobalPetrol Corp dividend$-$paying stock is currently selling for $$6\mathrm{.}25.$ The stock price is $$80,$ the strike price is $$75,$ and a dividend of $$0\mathrm{.}40$ is expected in two months and $$0\mathrm{.}30$ in $20$ days. The risk$-$free interest rate is $10\%$ per annum for all maturities. Use $4$ decimals

a$)$ What opportunities are there for an arbitrageur? $(4$ marks$)$

b$)$ i$)$What payoff and profit opportunities are there for an arbitrageur If the stock price in the market at the end of $6-$months is $$82?(3$ marks$)$

ii$)$ Present the respective call position in a graph. $(3$ marks$)$