$*13-25.$ The demand for a product over the next five periods may be filled from regular production, overtime production, or subcontracting. Subcontracting may be used only if the overtime capacity has been used. The following table gives the supply, demand, and cost data of the situation.

The unit production costs for the three levels in each period are $\backslash (\backslash$$ $4,\backslash$$ $6\backslash ),$ and $\backslash (\backslash$$ $7\backslash ),$ respectively. The unit holding cost per period is $\backslash (\backslash$$ $\mathrm{.}50\backslash ).$ Determine the optimal solution.