The standard deviation of monthly changes in the spot price of live cattle is $($in cents per pound$)1\mathrm{.}2.$ The standard deviation of monthly changes in the futures price of live cattle for the closest contract is $1\mathrm{.}5.$ The correlation between the futures price changes and the spot price changes is $0\mathrm{.}9.$ It is now October $15.$ A beef producer is committed to purchasing $300,000$ pounds of live cattle on November $15.$ The producer wants to use the December live$-$cattle futures contracts to hedge its risk. Each contract is for the delivery of $40,000$ pounds of cattle. $(1)$What is the hedge ratio? $(2)$ How many futures contracts should the producer long or short?