Statistics: Practice Problems Solutions

1. (24 points) If needed, additional workspace is provided on the undermentioned sheet. Doug Moodie is the hot seat of Garden Products Limited. Over the last 5 years, his vice chairman of marketing has been providing the gross sales guess using his special contract forecasting technique. The actual sales for the historical ten years and the forecasts from the vice president of marketing be given below. form Sales VP/Marketing Forecast 1 170,300 2 168,250 3 165,700 4 169,000 5 168,000 6 167,300 170,000 7 175,250 170,000 8 172,ergocalciferol 180,000 9 156,700 180,000 10 176,300 160,000 Doug wonders if perhaps a weight down mournful amount or an exp whizntial function smoothing approach to forecasting might be better than having the vice president of arketing mark the forecast. Doug necessitys to evaluate a twain-period charge locomote bonny with weights of 0. 7 and 0. 3 for the or so young and side by side(p) most recent periods. He like wise wants to evaluate the exponential smoothing with an ? = 0. 3 and a starting forecast for period 6 of 168,000 units. a) Which of the three methods (weighted moving average, exponential smoothing and VP/Marketing) provides the best forecasting method if you were to evaluate these methods for their forecasting accuracy for eld 8 through 10. Use one of the evaluation methods we have discussed. keep an eye on next page b) In part a) we determine which is the best method of those three methods.However, would you remember using this method for forecasting sales for socio-economic class 11? Why or Why not? See next page c) What would be the forecast for Year 11 using both the weighted moving average and the exponential smoothing methods? See next page pic 2. (23 points) Lake Charles Seafood makes 500 woody packing boxes for fresh seafood per sidereal day, working in two 10- mo shifts. The marketing department has certain that demand has increased so that 650 woody boxes for f resh seafood are required daily. collectible to higher demand, plant managers are considering carrying outal three 8-hour shifts instead. Productivity is measured in terms of boxes fired per hour worked. ) puzzle out the productiveness of the ope proportionalityn for the two-shift operation producing 500 boxes. 500/20 = 25 boxes per hour b) Calculate the productivity of the operation for the three-shift operation producing 650 boxes. 650/24 = 27. 08 c) Using the two-shift operation as the base, get the percentage difference between the two-shift operation and the three-shift operation as described in parts a) and b). (27. 08-25)25 = 1. 083 or an increase of 8. 3% d) Now suppose that the plant managers want to be able to produce the 650 boxes scarcely only use two 10-hour shifts. What must(prenominal) the productivity be to achieve this output signal output? 650/20 = 32. 50 boxes per hour ) If the company believes that to be belligerent if it is to produce 650 wooden boxes , the company must wrap up a productivity measure of 40 boxes per hour. What are the maximum hours a day the company grass work? 650/x = 40 X = 16. 25 hours 3. (19 points) spare workspace is provided on the next page. Students in a science class have reasonable received their grades on the first bear witness. The instructor has provided information about the first test grades in some previous classes as well as the closing average for the same students. Some of these grades have been sampled and are as follows Student 1 2 3 4 5 6 7 8 9 inaugural Test Grade 98 77 88 80 96 61 66 95 69 utmost Average 93 78 84 73 84 64 64 95 76 You are also provided the results from several different linear reversal affinitys for the above data. These provide different regress relationships looking at different combining of independent and dependent variables. pica) Develop a linear lapsing model that seat be used to predict the last-place course average based on the first test grade. pic b) Predict the lowest average of a student who make an 83 on the first test. pic c) Would you remember using this relationship for forecasting the final averages? Why? Also, explain how strong the relationship is between these two variables. pic d) Suppose a student scored a 38 on the first test. Predict the final average of a student who had this score?What cautions would you pep up about using the linear regression relationship for predicting a final average? pic 4. (18 points) David Upton is president of Upton manufacturing, a producer of Go-Kart tires. Upton makes 1,000 tires per day with the following resources Labor400 hours at $12. 50 per hour Raw sensible20,000 pounds per day at $1. 00 per pound cypher$5,000 per day Capital$10,000 per day a) What is the attention movement productivity for these tires at Upton Manufacturing expressed per labor hour? Labor productivity = chiliad tires/400 hours = 2. 5 tires/hour. b) What is the multi-factor (total factor) producti vity expressed per dollar? headmaster Multifactor productivity is universal gravitational constant tires/(400 ? $12. 50 + 20,000 ? $1 + $5,000 + $10,000) = ,000 tires/$40,000 = 0. 025 tires/dollar. c) What is the percent change in the total factor productivity if Upton can reduce the energy snout by $1,000 without cutting production or changing any separate inputs? Original Multifactor productivity is 1000 tires/(400 ? $12. 50 + 20,000 ? $1 + $5,000 + $10,000) = 1,000 tires/$40,000 = 0. 025 tires/dollar. Revised Multifactor productivity changes from 1,000/40,000 to 1,000/39,000, or from 0. 025 to 0. 02564 The ratio is 1. 0256, so the change is a 2. 56 percent increase. 5. (16 points) a) curtly discuss two ways that operations management can provide a company with a competitive value. 8 points Open-ended answerSupports the other functions, part withs what is promised to the customer provides a competitive advantage provides a low cost plectron plan and execute the production and preservation of the firms goods and services Ops Mgt is defined as the design, operation, and improvement of the systems that create and deliver the firms primary products and services. b) Briefly discuss two of the major issues that are facing operations management faculty in the current business environment. 8 points Open-ended answer Global challenge, mechanisation and technology, commoditization of the supplier, coordinating the relationships between mutually confirming but separate organizations, optimizing global supplier, production, and scattering networks, increased co-production of goods and services, managing customer touch points, height senior management awareness of operations as a significant competitive weapon.