At a hydrocarbon processing factory, process control involves periodic analysis of samples for a certain process quality parameter. The analytic procedure currently used is costly and time consuming. A faster and more economical alternative procedure has been proposed. However, the numbers for the quality parameter given by the alternative procedure are somewhat different from those given by the current procedure, not because of any inherent errors but because of changes in the nature of the chemical analysis. Management believes that if the numbers from the new procedure can be used to forecast reliably the corresponding numbers from the current procedure, switching to the new procedure would be reasonable and cost effective. The following data were obtained for the quality parameter by analyzing samples using both procedures: Current (Y) Proposed (X) Current (Y) Proposed (X) 2.8 3.2 3.1 3.1 3.7 3.8 2.6 3.0 2.8 3.5 3.3 3.6 3.6 4.0 3.4 4.0 3.6 3.7 2.1 2.6 2.7 3.6 3.2 3.2 3.3 3.5 3.1 2.7 a. Use linear regression to find a relation to forecast Y, which is the quality parameter from the current procedure, using the values from the proposed procedure, X. The forecasting model is given by the equation Y = + X. (Enter your responses rounded to three decimal places.)

At a hydrocarbon processing factory, process control involves periodic analysis of samples for a certain process quality parameter. The analytic procedure currently used is costly and time consuming. A faster and more economical alternative procedure has been proposed. However, the numbers for the quality parameter given by the alternative procedure are somewhat different from those given by the current procedure, not because of any inherent errors but because of changes in the nature of the chemical analysis. Management believes that if the numbers from the new procedure can be used to forecast reliably the corresponding numbers from the current procedure, switching to the new procedure would be reasonable and cost effective. The following data were obtained for the quality parameter by analyzing samples using both procedures: Current (Y) Proposed (X) Current (Y) Proposed (X) 2.8 3.2 3.1 3.1 3.7 3.8 2.6 3.0 2.8 3.5 3.3 3.6 3.6 4.0 3.4 4.0 3.6 3.7 2.1 2.6 2.7 3.6 3.2 3.2 3.3 3.5 3.1 2.7 a. Use linear regression to find a relation to forecast Y, which is the quality parameter from the current procedure, using the values from the proposed procedure, X. The forecasting model is given by the equation Y = + X. (Enter your responses rounded to three decimal places.)

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter9: Decision Making Under Uncertainty

Section9.2: Elements Of Decision Analysis

Problem 2P

See similar textbooks

Similar questions

The Tinkan Company produces one-pound cans for the Canadian salmon industry. Each year the salmon spawn during a 24-hour period and must be canned immediately. Tinkan has the following agreement with the salmon industry. The company can deliver as many cans as it chooses. Then the salmon are caught. For each can by which Tinkan falls short of the salmon industrys needs, the company pays the industry a 2 penalty. Cans cost Tinkan 1 to produce and are sold by Tinkan for 2 per can. If any cans are left over, they are returned to Tinkan and the company reimburses the industry 2 for each extra can. These extra cans are put in storage for next year. Each year a can is held in storage, a carrying cost equal to 20% of the cans production cost is incurred. It is well known that the number of salmon harvested during a year is strongly related to the number of salmon harvested the previous year. In fact, using past data, Tinkan estimates that the harvest size in year t, Ht (measured in the number of cans required), is related to the harvest size in the previous year, Ht1, by the equation Ht = Ht1et where et is normally distributed with mean 1.02 and standard deviation 0.10. Tinkan plans to use the following production strategy. For some value of x, it produces enough cans at the beginning of year t to bring its inventory up to x+Ht, where Ht is the predicted harvest size in year t. Then it delivers these cans to the salmon industry. For example, if it uses x = 100,000, the predicted harvest size is 500,000 cans, and 80,000 cans are already in inventory, then Tinkan produces and delivers 520,000 cans. Given that the harvest size for the previous year was 550,000 cans, use simulation to help Tinkan develop a production strategy that maximizes its expected profit over the next 20 years. Assume that the company begins year 1 with an initial inventory of 300,000 cans.
OPERATIONS RESEARCH TWO Sakala is interested in developing and marketing a new drug. The cost of extensive research to develop the drug would be K100,000. The manager of research programme said that there is 60% chance that the drug will be developed successfully. The market potential is assessed as follows with present value of profit: Market conditions Probability Present value of profits (K) Large market potential 0.1 500,000 Moderate market potential 0.6 220,000 Low market potential 0.3 80,000 The present value figures do not include the cost of research. While Mr. Sakala was considering this proposal, another similar proposal came up which also required the investment of K100,000 .The present value of profit for the second proposal wasK120,000. The return on the investment in the second proposal is almost certain. Draw a decision tree for Mr. Sakala indicating all choices and events What decision Mr. Sakala should take regarding the…
Peter sells backpacks at a kiosk in the mall. He knows the back-to-school rush will start in August, and he wants to determine whether the increase in customer traffic at the mall will increase his sales revenue and, if so, by how much? Using Sensitivity analysis.
Refer to Problems 1 and 2. Construct a graph that will enable you to perform sensitivity analysis on the problem. Over what range of P(high) would the alternative of doing nothing be best? Expand? Subcontract?
Aqua Man Company manufactures and sells a single product. Planned and actual production in its first year of operation was 100,000 units. Planned and actual costs for the year were as follows: Manufacturing Non-manufacturing Variable P600,000 P500,000 Fixed P400,000 P300,000 The company sold 85,000 units of product at a selling price of P30 per unit. Using absorption costing, the company’s operating profit was Select one: a. P1,020,000 b. P975,000 c. P900,000 d. P750,000
Figure shows summer air visibility measurements for Denver, Colorado. The acceptable visibility standard is 100, with readings above 100 indicating clean air and good visibility, and readings below 100 indicating temperature inversions caused by forest fires, volcanic eruptions, or collisions with comets.a. Is a trend evident in the data? Which time-series techniques might be appropriate for estimating the average of these data?b. A medical center for asthma and respiratory diseases located in Denver has great demand for its services when air quality is poor. If you were in charge of developing a short-term (say, 3-day) forecast of visibility, which causal factor(s) would you analyze? In other words, which external factors hold the potential to significantly affect visibility in the short term?c. Tourism, an important factor in Denver’s economy, is affected by the city’s image. Air quality, as measured by visibility, affects the city’s image. If you were responsible for development of…
A town's department of public works is concerned about adverse public reaction to a sewer project that is currently in progress. Because of this, the Commissioner of Public Works has authorized a weekly survey to be conducted of town residents. Each week, for a total of 10 weeks, a sample of 100 residents is questioned on their feelings towards the project. Number of responndets who opposed (each week, respectively): 7, 20, 18, 12, 20, 20, 6, 19, 24, 24.Analyze this data using an appropriate control chart (three sigma control limits). Is the community sentiment stable? a. Unstable, 3 observations out of control b. Unstable, 1 observation out of control c. Unstable, 2 observations out of control d. Stable
Gotham City has 10,000 streetlights. City investigatorshave determined that at any given time, an average of 1,000lights are burned out. A streetlight burns out after an averageof 100 days of use. The city has hired Mafia, Inc., to replaceburned-out lamps. Mafia, Inc.’s contract states that thecompany is supposed to replace a burned-out street lamp inan average of 7 days. Do you think that Mafia, Inc. is livingup to the contract?
What is linear regression? Can linear regression be automatically calculated in SPSS?
Mike Thatcher is a sales manager for an automobile dealership in Alberta. Mike earns a bonus each year based on revenue generated by the number of vehicles sold in the year less related warranty expenses. The quality of automobiles sold each year seems to vary since the warranty experience related to vehicles sold is highly variable. The actual warranty expenses have varied over the past 10 years from a low of 3% of an automobile’s selling price to a high of 10%. In the past, Mike has tended toward estimating warranty expenses on the high end just to be prudent. It is the end of the year and once again he must work with the dealership’s accountant in arriving at the warranty expense accrual for the cars sold this year. Required 1. Does the warranty accrual decision present any kind of ethical dilemma for Mike Thatcher? 2. Since the warranty experience is not constant, what percent do you think Mike should choose for this year? Justify your response.
Mr. A wants to analyze the CGPA of bachelor's students for the years 2011, 2012, 2013. Is she conducting a cross sectional study? True false
Based on a sample of 80 recent MBA graduates (40 male and 40 female), the following information was made available regarding their annual salaries. The standard deviation of salaries for the male graduates was $40,000 and that for the female graduates was $25,000. a.) For the male graduates, what is the probability of obtaining a sample mean salary within $10,000 of the population mean? Show work. b.) Consider the same question in (a) but for the female graduates. In which case, males or females, do we have a higher probability of obtaining a sample estimate within $10,000 of the population mean? Why? Show work. c.) Suppose that the sample mean salary of females is $125,000. Develop a 95% confidence interval estimate for the mean salary of all female graduates.