A trader owns $100,000$ units of a particular commodity and decides to hedge the value of her position with futures contracts on another related asset. Each futures contract of the commodity is $5,000$ units. The spot price of the asset that is owned is $$30$ and the standard deviation of the change in this price over the life of the hedge is estimated to be $$0\mathrm{.}56.$ The futures price of the related asset is $$28$ and the standard deviation of the change in this over the life of the hedge is $$0\mathrm{.}50.$ The coefficient of correlation between the spot price change of the commodity and futures price change is $0\mathrm{.}87.$

a$.$ What strategy should the trader use to protect the units of the commodity she owns? Clarify both the position she should take and quantity of futures contracts $($hint: hedge ratio$).6$ pts Show all work and clearly explain.