Rework problem $23$ in section $6\mathrm{.}3$ of your textbook $($page $276)$ except use the following data instead of the data in the textbook: Assume that the production of $1$ unit of magnesium requires $0\mathrm{.}2$ units of magnesium and $0\mathrm{.}5$ units of aluminum, and that the production of $1$ unit of aluminum requires $0\mathrm{.}6$ units of magnesium and $0\mathrm{.}5$ units of aluminum.

Find the production schedule that satisfies an external demand for $60$ units of magnesium and $40$ units of aluminum.