The standard deviation of monthly changes in price of cattle is $1\mathrm{.}2,$ the standard deviation of monthly changes in futures price of cattle is $1\mathrm{.}4,$ and the correlation between the two price changes is $0\mathrm{.}7.$ A ranch owner expects to sell $200$ cattle in a month and wants to use cattle futures contracts to hedge its risk. If each contract is for delivery of $5$ cattle, the owner should

$($a$)$ short $40$ contracts $($b$)$ short $24$ contracts $($c$)$ short $9$ contracts

$($d$)$ buy $24$ contracts $($e$)$ buy $40$ contracts