Please show all your steps.

1) A barrel of West Texas Intermediate crude oil currently trades for $70 in the spot market. A contract to deliver 1000 barrels of oil 6 months from today currently trades at a forward price of $82 per barrel. It will cost $10 per barrel to store oil for 6 months, payable at the end of the storage period. You have access to risk-free borrowing and lending at a 3% interest rate. a) Use a replicating portfolio to derive the no-arbitrage forward price for delivery 6 months from today. Be sure to use a payoff table to show that your two portfolios have the same payoffs. b) Based on your results in part a), there is an arbitrage opportunity. Construct a set of transactions today that costs nothing today, but generates a guaranteed positive cash flow 6 months from today. Prove both: zero cost today, riskless future profit