A large food chain owns a number of pharmacies that operate in a variety of settings. Some are situated in small towns and are open for only 8 hours a day, 5 days per week. Others are located in shopping malls and are open for longer hours. The analysts on the corporate staff would like to develop a model to show how a store’s revenues depend on the number of hours that it is open. They have collected the following information from a sample of stores. Hours of Operation Average Revenue ($) 40 5958 44 6662 48 6004 48 6011 60 7250 70 8632 72 6964 90 11097 100 9107 168 11498 Use a linear function (e.g., y = ax + b; where a and b are parameters to optimize) to represent the relationship between revenue and operating hours and find the values of the parameters using the nonlinear solver that provide the best fit to the given data. What revenue does your model predict for 120 hours? Suggest a two-parameter nonlinear model (e.g., y = axb; where a and b are parameters to optimize) for the same relationship and find the parameters using the Nonlinear Solver that provide the best fit. What revenue does your model predict for 120 hours? Which if the models in (a) and (b) do you prefer and why?

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter4: Linear Programming Models

Section: Chapter Questions

Problem 50P

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A large food chain owns a number of pharmacies that operate in a variety of settings. Some are situated in small towns and are open for only 8 hours a day, 5 days per week. Others are located in shopping malls and are open for longer hours. The analysts on the corporate staff would like to develop a model to show how a store’s revenues depend on the number of hours that it is open. They have collected the following information from a sample of stores.

Use a linear function (e.g., y = ax + b; where a and b are parameters to optimize) to represent the relationship between revenue and operating hours and find the values of the parameters using the nonlinear solver that provide the best fit to the given data. What revenue does your model predict for 120 hours?

Suggest a two-parameter nonlinear model (e.g., y = ax^b; where a and b are parameters to optimize) for the same relationship and find the parameters using the Nonlinear Solver that provide the best fit. What revenue does your model predict for 120 hours? Which if the models in (a) and (b) do you prefer and why?

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