Questiоn 27: Minimum-vаriаnce futures hedge A firm expects tо purchаse 120,000 barrels оf a commodity in six months. A related futures contract covers 1,000 barrels. The correlation between changes in the firm's spot purchase price and the futures price is 0.80. The standard deviation of spot-price changes is 30%, and the standard deviation of futures-price changes is 25%. The firm establishes the minimum-variance hedge when the futures price is $82 per barrel. At maturity, the futures price is $90 and the firm's physical purchase price is $92. Using the nearest whole number of contracts, which pair is closest to the hedge position and the effective price per physical barrel after futures gains?