Q $3)$ b$)$ There are a call and a put option contract available for $1,000,000$ pounds of coffee with an expiration date in three months. The strike price is $$2$ and the premium for the put is $$20$ for $10,000$ pounds of coffee and the premium for the call is $$30\mathrm{.}00$ for $10,000$ pounds of coffee. Show the cash flows of the option contracts, of the underlying transaction and of the hedge strategy if the spot price of coffee on the delivery date is $$1\mathrm{.}5,$ $$2$ or $$2\mathrm{.}5.$ Explain how you can hedge your position $($with the call or the put option$)$ against the rise in the price of coffee.