Assignment:
Consider a situation where a particular product is produced and placed in in-process inventory until it is needed in a subsequent production process. The number of units required in each of the next 3 months, the setup cost, and the regular-time unit production cost (in units of thousands of dollars) that would be incurred in each month are as follows:
| Month |
Requirement |
Setup Cost |
Regular time unit Cost |
| 1 |
1 |
5 |
8 |
| 2 |
3 |
10 |
10 |
| 3 |
2 |
5 |
9 |
There currently is 1 unit in inventory, and we want to have 2 units in inventory at the end of 3 months. A maximum of 3 units can be produced on regular-time production in each month, although 1 additional unit can be produced on overtime at a cost that is 2 larger than the regular-time unit production cost. The holding cost is 2 per unit for each extra month that it is stored. Use dynamic programming to determine how many units should be produced in each month to minimize the total cost.
Provide complete and step by step solution for the question and show calculations and use formulas.