It Costs $12 to Make a Single Unit Using Regular

It costs $12 to make a single unit using regular production and $15 to make a single unit using overtime production. Total overtime production is limited to 500 units for the five-month period. The manufacturing plant has a regular production capacity of 250 units per month and 50 units in inventory at the start of the planning period. There is a $5 per unit charge for holding inventory at the end of each month and a limit of 250 units ending inventory for any period. Develop an objective function and constraints to solve this problem.
$$\begin{array} { | l | c | } \hline { \text { Month } } & \text { Forecast } \\\hline \text { Fanuary } & 250 \\\hline \text { February } & 200 \\\hline \text { March } & 300 \\\hline \text { April } & 400 \\\hline \text { May } & 500 \\\hline\end{array}$$