$5.$

A $\backslash (10-$m$^\{3\}\backslash )$ compartment is available for storing three items. The volumes needed to store $1$ unit of items $1,2,$ and $3$ are $3,2,$ and $\backslash (4\backslash$mathrm$\{$~m$\}^\{3\}\backslash ),$ respectively. The probabilistic demand for the items is described in the following table. The shortage costs per unit for items $1,2,$ and $3$ are $\backslash (\backslash$$ $8,\backslash$$ $10\backslash ),$ and $\backslash (\backslash$$ $15\backslash ),$ respectively. How many units of each item should be held in the compartment?