1. Company X is expected to purchase 169,000 pounds of a lemon juice in the 4 months from now and would like to hedge its exposure. Unfortunately, there is no future contracts offered for limon juice; however, company X decided to use orange future contacts to hedge its exposure on lemon juice since the prices of orange and lemon juices are highly correlated. Each orange juice contract traded by the CME Group is on 15,000 pounds of orange juice. The below table shows the monthly changes in the spot price of lemon juice and the futures price of orange.

Use the data to calculate:

1. The minimum variance hedge ratio. (Show your work, use the formula, do not use excel)
2. The optimal number of future contracts for hedging
3. Suppose that the future price on orange juice is $1.35/pounds and the spot price for lemon juice is $1.1/pound, what is the optimal number of future contracts for hedging after tailing the hedge.