$10\mathrm{.}14.$ The price of a European call that expires in six months and has a strike price of $$30$ is $$2.$ The underlying stock price is $$29,$ and a dividend of $$0\mathrm{.}50$ is expected in two months and again in five months. Risk$-$free interest rates for all maturities are $10\%.$ What is the price of a European put option that expires in six months and has a strike price of $$30?$

$10\mathrm{.}15.$ Explain carefully the arbitrage opportunities in Problem $10\mathrm{.}14$ if the European put price is $$3.$