Create a Minimum Cost Chase Plan for the Forecast Shown

Create a minimum cost chase plan for the forecast shown in the table. There is no beginning inventory and regular production capacity is 350 units. Overtime costs $20 extra and is limited to 50 units per month and subcontracting is limited to 100 units per month and costs $15 per unit. Back orders cost $40 per unit and there is a cost of $5 per month to hold a unit in inventory. There is room for only 100 units in inventory. What is the total plan cost above regular production cost?
$$\begin{array} { | l | c | l | l | l | l | } \hline { \text { Month } } & \text { Forecast } & \text { Regular } & \text { Overtime } & \text { Subcontracting } & \begin{array} { c } \text { Ending } \\\text { Inventory }\end{array} \\\hline \text { January } & 250 & & & & \\\hline \text { February } & 400 & & & & \\\hline \text { March } & 500 & & & & \\\hline \text { April } & 350 & & & & \\\hline\end{array}$$