Please show the detailed calculation and formula you used.

A cocoa merchant holds current inventory of cocoa worth $10 million at present price of $1250 per metric ton. The variance of returns from the cocoa inventory ()is 0.073. She is considering hedging her inventory with futures. However, there are no futures contracts available on cocoa, so she decides to use coffee futures to hedge her exposure. The variance of the coffee futures () is 0.109. For the particular grade of cocoa in her inventory, the correlation between the futures and spot is 0.85. The futures contract size is 10 metric tons.

a. What is minimum variance hedge ratio? Why do we need it? Explain.

b. What should the merchant do to hedge her exposure? Calculate and explain