are157-hwk1

are157-hwk1 - ARE 157 Spring 2008 M.Whitney ANALYSIS FOR...

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Unformatted text preview: ARE 157 Spring 2008 M.Whitney ANALYSIS FOR PRODUCTION MANAGEMENT Homework 1 Due Tuesday, April 15th, at start of class 1. (12) Simon is a quality control inspector for Chico Cookies. He has collected samples of cookies produced by two of the firm’s packaging machines, as shown below. The firm’s cookies are packaged in bags labeled as containing 16 ounces. In order to ensure that no customers are shorted, the firm requires that each bag contains at least 16 ounces, with a target of 16.15 ounces and an upper limit of 16.30 ounces. Machine A Machine B 2 bags contained 16.10 . 1 bag contained 16.00 9 bags contained 16.15 14 bags contained 16.10 10 bags contained 16.20 8 bags contained 16.20 4 bags contained 16.25 2 bags contained 16.25 a. (1) Afler looking at the 2 samples above, Simon’s coworker, Denise, concluded that both machines are operating satisfactorily, since none of the sampled bags are out of tolerance. Explain why this is not a satisfactory criterion for quality control purposes. b. (8) Find the mean and sample standard deviation of each sample. What are the largest and smallest weight that is expected to occur for each machine, assuming a normal distribution? c. (3) Is Machine A operating satisfactorily at present? Is it capable of being controlled? Is Machine B operating satisfactorily at present? Is it capable of being controlled? Show how you know. What type of action, if any, should the firm take? 2. (10) Brad works in a factory that produces buttons. One of his duties is to monitor a machine that places buttons in packages labeled as “100 buttons”. The machine has worked satisfactorily in the past, so Brad monitors it using a mean control chart. Every hour he samples 5 packages of buttons and counts them. Here are the results of his last 4 hourly samples: pkg. hour 1 hour 2 hour 3 hour 4 1 104 103 105 101 2 102 103 103 102 3 102 102 104 104 4 104 102 104 105 5 L0} in m. an Xbar-9103 102 104 103 a. (2) Find the mean of sample means, “Xbarbar”. (Note: the mean of each sample is already shown) Also find the standard deviation of sample means, 0 '2, assuming the population standard deviation is o = 1.04. b. (4) What are the upper and lower 3-sigma control limits for this process? Is the mean of this process in control? Show or explain how you know. c, (4) How would your answer to part b change, if the finn’s management decided to implement 2-sigma mean control limits? 3. (16) Stanley Office Supply is considering whether to purchase flood insurance for its headquarters building in North Natomas, CA. The firm expects that in each year, there is a 1% chance of a major flood causing $3,000,000 in damage, and a 4% chance of a minor flood causing $500,000 in damage. The firm is considering 3 options to address this risk: Policy A costs $38,000/year. It has a deductible of $20,000, then pays for 75% of any damages above that amount. ' Policy B costs $42,000/year. It has no deductible, and pays for 80% of any damages. Self-insure. The firm pays for all its own damages should they occur. (a) (15) Develop a decision matrix that shows the actual dollar outcomes that can occur for each of the three options above, and their expected values. Also calculate the standard deviation for each option. (b) (1) If the firm is risk-neutral, which option should it choose? If the firm is highly risk- averse (preferring the option with the smallest standard deviation), then what strategy will it choose? 4. (6) Silveyville Natural Foods is deciding whether to open a second retail store, in addition to its existing one. The firm’s projected profits depend on the strength of the overall economy, as shown below: (numbers are in millions) economic activi Strong Average Weak expected stande strategy p=.2 p=.5 p=..3 value deviation I--- "-- Find the expected value and standard deviation for each strategy. Which strategy should the firm - select, assuming it is risk-neutral? Would the same choice still be best if the firm was highly risk—averse? 5. (6) Find and print out (or copy down) an example of (a) an effective mission statement; and (b) a poorly designed mission statement. Briefly describe why you think these mission statements are effective or inefi'ective,. taking into account the 2 criteria we mentioned in class. ...
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are157-hwk1 - ARE 157 Spring 2008 M.Whitney ANALYSIS FOR...

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