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##### QSO510 final exam

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solution

**Question**

Question;Directions: This exam consists of seven problems and is an open-book exam;with no time limit. All work should be done individually.Word-process your solutions within this;template and show all steps used in arriving at the final answers. Incomplete;solutions will receive partial credit. Copy and paste all necessary data from;Excel into this document and create tables as needed.;Problem;1;Suppose;a manufacturing company makes a certain item. The time to produce each item is;normally distributed around a mean of 27 minutes with a standard deviation of 2.5;minutes. Thus, the population of production times is normal in shape. Find the;mean and standard deviation of the sample.;Problem;2;The average prices for a product in 12 stores;in a city are shown below.;$2.99;$2.85, $3.25, $3.55, $3.00, $2.99, $2.76, $3.50, $3.20, $2.85, $3.75, $3.85;Test the hypothesis that the average price is;higher than $2.87. Use level of significancea;= 0.05.;Problem 3;A store wishes;to predict net profit as a function of sales for the next year. The following;table gives the years 1998 to 2005.;Year;Sales;(thousands of;dollars);Net Profit;1998;51;5;1999;55;10.2;2000;65;9.6;2001;82;-3;2002;75;2.8;2003;71;3.2;2004;82;-2.3;2005;81;-2.6;(a) Graph;the points from 1998 through 2005 on a scatter diagram using Sales as the;independent variable and Net Profit as the dependent variable.;(b) Draw;the regression line on the graph you constructed in Part (a).;(c) What;is the value of the coefficient of determination for this regression model?;Comment on the strength of the regression line for this model.;(d) What;is the predicted net profit for 2006 if sales are expected to be 125?;Problem;4;Last week?s sales of iMac computers at an;Apple Store in Oklahoma City, OK, are shown in the following table;Day;Sales;(Dollars);1;180;2;150;3;210;4;225;5;195;6;190;7;230;(a) Use the 3-day;moving average method for forecasting days 4?7.;(b);Use the 3-day;weighted moving average method for forecasting days 4?7. Use Weight 1 day ago =;2, Weight 2 days ago = 4, and Weight 3 days ago = 3.;(c);Compare the;techniques using the mean absolute deviation (MAD).;Problem 5;The following table shows six years of average annual cost-of-living;index data;Year;Annual Cost of Living Index;2008;105.8;2009;111.4;2010;121.9;2011;134.3;2012;128.6;2013;125.2;(a);Forecast;the average annual food price index for all years from 2008 to 2013. Use a 3-year;weighted moving average with weights of 0.5, 0.3, and 0.2. Use the largest;weight with the most recent data.;(b);Forecast;the average annual food price index using exponential smoothing with?;= 0.7 for all years from 2008 to 2014. Use the rate for 2008 as the;starting forecast for 2008.;(c);Which;of the methods in parts (a) and (b) produces better forecasts for the 3 years;from 2011 to 2013? Answer on the basis of mean square error (MAD).;Problem;6;A company manufactures two products, Product A;and Product B. The wholesale price and manufacturing cost of each product are;shown below.;Item;Price;Cost;Assembly Times (hr);A;$30;$10;2;B;$45;$15;4;The company will produce a minimum of 5,000 of;each item. Given the number of hours, the company can sell no more than 8,000;of Item A and 10,000 of Item B. Suppose the company has 50,000 hours of;assembly time available. How many of each item should it produce in order to;maximize profits while meeting all necessary constraints? Give the LP model and;use the graphical method to find the optimal solution.;Problem;7;A commercial real estate company is evaluating;a proposed warehouse. The proposed site is near a rail terminal, but the state;government may extend the highway to the area. In addition, the federal;government is considering rebuilding the local port facilities. Below is the;payoff table in monthly profit depending upon what government actions are;taken. Based on the following criteria, what are the correct choices for;terminal rental?;(a) Optimistic or maximax;criterion;(b) Pessimistic or maximin;criterion;(c) Equally likely or;principle of insufficient reason criterion;Warehouse size (ft2);Development projects;Rail terminal only;Highway expansion;Port rehabilitation;All;15000;10;25;35;40;30000;15;25;40;50;60000;20;30;45;75;100000;15;20;40;90

Paper#50410 | Written in 18-Jul-2015

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