Anglo American Platinum Limited is a major worldwide producer of platinum. Platinum is widely used in the production of catalytic converter. It is now August 1. The company is committed to selling 600 ounces of platinum on September 14. To hedge the risk, the company is considering using October futures contracts to offset the risk exposure. The standard deviation of monthly changes in the spot price of platinum per ounce is 20 and the standard deviation of monthly changes in the futures price of the closest contract is 24. 

The correlation between the futures price changes and the spot price changes is 0.80. Each contract is for the delivery of 50 ounces platinum.

(a) What is the optimal hedge ratio?
(b) Should the hedger take a long or short futures position?
(c) What is the optimal number of futures contracts with the hedge?