Mathematical Model $($continued$)$:

$$ Constraints are defined as the following balance equation:

Beginning inventory$+$Production amount $$ Ending inventory $=$ Demand x$1$ I$1=100($Month $1)$

$100440$

$0140220110$

Figure $5$: Optimum solution of the production$-$inventory problem

I$1+$x$2$I$2=250$

I$2+$x$3$I$3=190$

I$3+$x$4$I$4=140$

I$4+$x$5$I$5=220$

$($Month$2)($Month$3)($Month$4)($Month$5)$

It replace xt