Problem 1 (25 points) A factory is planning its production for the next. six months. No stock-out is allowed (i.e., all demands have to be served in the same period they arrive). The factory can use an unlimited amount of overtime. Capacity of regular-hour production is 10 units per-month. There is no initial inventory. The cost of carrying one unit of inventory from one month the next. is h. The cost of producing a unit overtime is 1.8. Demands in the next six months are Question: - (5 points) formulate a linear program model for determining the optimal production plan (you can use h as the inventory cost). - (15 points) use whichever method (software) you are comfortable with to solve the linear program for h=0.5,1,1.5, and 2 . - (5 points) as h increases, how do the overtime cost, the inventory cost, and the total cost change, and why