discounts are available. The maximum order size is $1,000$ units.

$Y_t=\{\begin{array}{ccc}1& ifan\text{o}\text{r}\text{d}\text{e}\text{r}is\text{p}\text{l}\text{a}\text{c}\text{e}\text{d}at\text{t}\text{h}\text{e}\text{s}\text{t}\text{a}\text{r}\text{t}of\text{p}\text{e}\text{r}\text{i}\text{o}\text{d}t\text{f}\text{o}\text{r}t=1,2,3,\text{d}\text{o}\text{t}\text{s}\text{,}& 12.\\ 0& \text{o}\text{t}\text{h}\text{e}\text{r}\text{w}\text{i}\text{s}\text{e}& \end{array}$

Min$1,(x_1+x_2+$dots$+x_{12})+(,)(H_1+H_2+$dots$+H_{12})+(150)(Y_1+Y_2+$dots$+Y_{12})$

s$.$t$.$

Period $1$ Demand

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Period $12$ Demand

$x_t(,)Y_t$ for $t=1,2,3,$dots,$12$