An retail firm has to deliver products during the next four weeks. in week 1, 200 products; week 2, 300 products; week 3, 300 products; week 4, 400 products. For each output produced during months 1 and 3, a $10 changing cost is incurred; for each output produced during months 2 and 4, a $12 changing cost is incurred. The inventory cost is $1.5 for each product in stock at the end of a month. The cost of setting up during a month is $200. The products are produced in by 100 batches for each week. Given that the initial inventory level is 0 units, use dynamic programming to determine an optimal production schedule