A gold$-$mining firm is concerned about short$-$term volatility in its revenues. Gold currently sells for $$1,350$ an ounce, but the price is extremely volatile and could fall as low as $$1,250$ or rise as high as $$1,450$ in the next month. The company will bring $1,150$ ounces of gold to the market next month.

a$.$ What will be the total revenues if the firm remains unhedged for gold prices of $($i$)$ $$1,250,($ii$)$ $$1,350,$ and $($iii$)$ $$1,450$ an ounce?

b$.$ The futures price of gold for delivery $1$ month ahead is $$1,360.$ What will be the firm$$s total revenues if the firm enters into a $1-$month futures contract to deliver $1,150$ ounces of gold?

c$.$ What will be the total revenues if the firm buys a $1-$month put option to sell gold for $$1,150$ an ounce? The put option costs $$33$ per ounce.