First, consider what kind of option you would buy to insure against loss due to change in exchange rate.

1)  If you lose money when the exchange rate goes up, you buy a call.
2)  If you lose money when the exchange rate goes down, you buy a put.

In your question, you would like to receive at least $800,000.  (500,000 pounds * $1.6/pound = $800,000)  Therefore, you want to buy the right to sell at least $1.6/pound at the end of 6 months.  -> Scenario 2

懂了，thank you very much.

I am still a little confused. Below is what I think.
People buy a call in the hope that the price of the underlying asset will rise. When the price of the underlying asset declines, the call buyer can choose not to exercise the call, therefore, protecting himself against the loss from price decline.
Similarly, the put buyer can choose not to exercise the put when the price of the underlying asset increases to the extent that K-S(t)<0, which is S(t)-K>0. Therefore, when S(t) rises too much, the put will be of no use. So, a put option protect against the loss from the increase in price.
For my question, there will be no loss if the exchange rate increases.......

Thank you very much if you can shed more light onto this problem.

Yes, options are not forced to exercise.  But the put option is to protect against loss from the decrease in price which is the decrease in exchange rate in this question.

1) When S(t) >= $1.6/pound, the pounds received from sales will be equal to or greater than $800,000. We won't execrise the put option.

2) When S(t) < $1.6/pound, the pounds will be less than $800,000.  If we exerise the put option, we will receive $800,000 which is the objective in this question.

I think you mixed up the defiinition of call and put options.

u guys are smart
~!