Golddiggers is a gold$-$mining firm planning to mine and sell $100,000$ ounces of gold over the next year. The fixed cost is $$330/$oz and variable cost is $$50/$oz$.$ The management makes the following forecasts for gold price in one year: $$350,$ $$400,$ $$450,$ and $$500.$ Answer the following questions. Also, do not add interest to the cost of production. Adjust only the option prices$/$premiums for interest. Perform all analysis only for one ounce of gold. a$)$ Construct a table showing Golddiggerss unhedged profit$/$oz for different prices at expiration. Note that the total cost is the fixed cost$/$oz plus the variable cost$/$oz$.(3$ points$)$ b$)$ Suppose Golddiggers is interested in hedging the price risk by entering into a forward contract. Should Golddiggers buy or sell the forward contract? Explain. $(3$ points$)$ c$)$ Suppose Golddiggers sells a forward contract at a forward price of $$420/$oz$.(5$ points$)$ i$.$ How much does it cost to enter into the above short forward contract? ii$.$ Compute the profit from the short forward position and the hedged profit. Note that profit from the hedged position includes the profit from the unhedged position $($only long gold$)$ and the profit from the short forward position $($only short forward$).$ iii. What is the maximum profit potential from the hedged position? iv$.$ Draw a profit diagram for both hedged and unhedged profit.