Worst case analysis ii Root sum of squares 0747 0995 1121 0005 2868 0026 2894

# Worst case analysis ii root sum of squares 0747 0995

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i. Worst case analysis ii. Root sum of squares ? ?𝑖? = 0.747 + 0.995 + 1.121 + 0.005 = 2.868 𝑋 = 0.026 → ? = 2.894 ± 0.026 → ? = 0.019 ± 0.014 𝑡𝑜𝑙 𝐷 = 0.003 2 + 0.005 2 + 0.004 2 + 0.014 2 = 0.0179 ( I ) → ? = 2.894 ± 0.0179 ( II ) ? ?𝑎𝑥 = 0.753 + 1.005 + 1.129 + ? ?𝑎𝑥 = 2.920 → ? ?𝑎𝑥 = 0.033

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Problem 4 A marketing company intends to lease a high end printer. Currently the company bulk orders to Kinko’s being charged a fixed shipping of \$10 each time an order is placed and the rate of \$0.1 per page for printing. You need to help the company answer the following questions: (Parameters: Lease = \$500 a month; Maintenance contract = \$ 100 per month; Toner = \$ 80 and prints 1000 pages; Paper = \$20 packets for 1000 pages; Constant demand for printing = 100 pages per day)
Problem 4A Given the parameters and assuming the company orders to Kinko’s on a daily basis, is it worth leasing a new high end printer? (please show assumptions and steps clearly) For leasing a high end printer: Fixed cost: 500 + 100 = 600 Variable cost: 80 1000 + 20 1000 × 30 × 100 = 300 Total cost: 900 For Kinko’s: Total cost: 10 × 30 + 0.1 × 100 × 30 = 600 No, it is preferable to continue ordering from Kinko’s.

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Problem 4B If the company was intending to continue ordering from Kinko’s, this would result in pages being printed late. This causes inconvenience to the employees. Often this inconvenience may be represented as a penalty. Consider we impose a penalty of \$0.1 per page per day for not having printed the page immediately. Find the optimal order quantity. Inconvenience cost: 𝑄 2 ? Fixed cost: ? + 𝑐𝑄 Total cost: ? + 𝑐𝑄 + ℎ 𝑄 2 ? Cost per unit time: ?+𝑐𝑄 ? + ℎ 𝑄 2 𝑄 = 2?? = 2 × 10 × 100 0.1 = 141.42 EOQ model:
Problem 5 Consider the assembly piece shown in the diagram below. If all the links A, B and C are of length 10 and standard deviation 0.2, calculate the mean length and standard deviation of link D. (Please show your work for full credit) ? = 𝑓 ?, ?, ? = ? cos 𝜋 4 + ? + ? cos 𝜋 4 ? = 𝑓 ?, ?, ? = ҧ ? cos 𝜋 4 + ? + ҧ ? cos 𝜋 4 = 10 cos 𝜋 4 + 10 + 10 cos 𝜋 4 = 24.14 ?𝑎𝑟 ? = 𝜕𝑓 𝜕? 2 ?𝑎𝑟 ? + 𝜕𝑓 𝜕? 2 ?𝑎𝑟 ? + 𝜕𝑓 𝜕? 2 ?𝑎𝑟(?) 𝜎 𝐷 = cos 𝜋 4 2 × 0.2 2 + 1 2 × 0.2 2 + cos 𝜋 4 2 × 0.2 2 = 0.2828

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