A firm has to deliver the following number of one of its product (Product X) during the next three weeks; week 1, 200 radios; week 2, 100 radios; week 3, 400 products. For each product produced during weekss 1 and 2, a $11 variable cost is incurred; for each product produced during week 3, a $13 variable cost is incurred. The inventory cost is $2.50 for each product in stock at the end of a week. The cost of setting up for production during a week is $300. Products made during a week may be used to meet demand for that week or any future week. Assume that production during each month must be a multiple of 100. Given that the initial inventory level is 0 units and maximum storage capcity is 400 units, use dynamic programming to determine an optimal production schedule.