Custom Fire (CF) produces a wide range of high-end custom-designed fireplaces for large houses and mansions in make-to- order fashion. Customers choose a product from firm's website and place their orders through the site. All products go through several stages of production, including fabrication, assembly, packaging, etc. The average time it takes for an order to go through these several stages and be completed is about 3 days with standard deviation of 0.5 days. The completed orders are shipped the same day. Table 2.7 shows the time that CF finished their last 30 orders. The completion time of the last fireplace produced before the first one in the table was at 8:00 am on Monday. Table 2.7 Production Completion Times of Last 30 Fireplaces at Custom Fire Production completion No. 1 2 3 4 5 6 7 8 9 10 Production completion Day Monday Monday Monday Monday Monday Monday Monday Monday Tuesday Tuesday Time 10:20 am 12:10 pm 1:28 pm 3:35 pm 5:24 pm 6:59 pm 8:28 pm 10:45 pm 12:50 am 2:54 am No. 11 12 13 14 15 16 17 18 19 20 Day Tuesday Tuesday Tuesday Tuesday Tuesday Tuesday Tuesday Tuesday Tuesday Tuesday Time 4:25 am 6:39 am 8:49 am 10:11 am 11:55 am 1:47 pm 3:20 pm 5:27 pm 6:57 pm 8:13 pm No. 21 22 23 24 25 26 27 28 29 30 Production completion Day Tuesday Wednesday Wednesday Wednesday Wednesday Wednesday Wednesday Wednesday Wednesday Wednesday Time 10:19 pm 12:14 am 2:20 am 4:25 am 6:34 am 9:06 am 11:01 am 1:07 pm 3:33 pm 5:22 pm The firm receives different number of orders in different days and it works on them in a first-come-first-served basis. The data shows that the number of outstanding orders in the last 6 months was never above 72. a. Managers of CF would like to add a delivery guarantee date to their website promising customers that their orders will be delivered within 6 days after they place their orders (assume each customer orders one fireplace). If the firm adds that to its website, what would be the maximum fraction of customers who will receive their orders beyond the promised date of 6 days? b. After weeks of discussion, CF managers came to the conclusion that announcing the same due date of 6 days to all customers without considering the status of their factory (i.e., the number of outstanding orders in the factory) is not a good strategy. Also, they have started working with several construction companies that often order more than one fireplace for their big projects, which should be delivered to them in one shipment when they are all finished. The new strategy is to give individual delivery date to each customer depending on the status of the factory and the number of products in the customer order. CF managers all agree that the promised delivery date should be such that the firm satisfies its promises 95 percent of the time. Under this new policy, what due date the firm should promise to a customer