Problem 2 (14 points) The table below shows demand for your product in the next six months The system is empty at beginning. You can carry inventory to future months but no demand stock-out is allowed. The inventory carrying cost is $100 per month per unit. 1. (5 points) Suppose that your regular production capacity in each month is fixed at the same level. You have to fill all demands by regular production (no overtime is allowed, but you can carry inventory). Determine the minimum amount of regular production capacity that you need. 2. Suppose that your regular production capacity is 5 units per month and you can use unlimited overtime production for free (i.e., no capacity limit and no additional cost) to cover excess demands - (3 points) what is the minimum number of units you need to produce overtime? - (3 points) if you have all overtime production in the first month, what will be your inventory cost? ( 3 points) if you can carry out overtime production in at most two of the six months, which month(s) should you do it to minimize your inventory cost