A large local dinner is open each weekday from 6am until 8pm.  Each waitstaff begins his/her shift 6-hour shift either at 6am, 8am, 10 am, noon or 2pm.  To determine how many waitstaff should begin at each of the above 5 times, the owner, based on her knowledge of her customers, has determined the minimum number of waitstaff that is required during each 2- hour time slot to give her customers the service that they expect.  This information, along with the wages** that are paid to each waitstaff for the 6-hour shift that they work, appears in the following table.    Time slot              minimum required             wages for 6-hour shift **                  6am – 8am                           2                                              $70                 8am – 10am                         4                                              $60              10am – noon                           7                                              $75 noon – 2pm                          9                                              $70 2pm – 4pm                            5                                              $80 4pm – 6pm                            8                                              ----- 6pm -  8pm                           6                                              -----   **           Each wage per shift is based on when the waitstaff starts his/her shift.  For example, the $70 listed for the 6am – 8am time slot is the wages for those starting at 6am, and, the $60 listed for the 8am – 10am time slot is the wages for those starting at 8am, etc., etc.   Note:      No shifts start at 4pm or 6pm because they would not be able to work a full 6-hour shift   Using X1, X2, …, X5, to represent the number of waitstaff starting at 6am, 8am, … , 4pm, formulate what is being asked for so that the owner can minimize her daily wages while satisfying all her minimum requirements.  No ‘…’s are to be used anywhere in your formulations.   the objective function       the constraint for the 6am – 8am time slot       the constraint for the noon – 2pm time slot       the constraint for the 4pm – 6pm time slot       the constraint for the 6pm – 8pm time slot

MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
icon
Related questions
Topic Video
Question

A large local dinner is open each weekday from 6am until 8pm.  Each waitstaff begins his/her shift 6-hour shift either at 6am, 8am, 10 am, noon or 2pm.  To determine how many waitstaff should begin at each of the above 5 times, the owner, based on her knowledge of her customers, has determined the minimum number of waitstaff that is required during each 2- hour time slot to give her customers the service that they expect.  This information, along with the wages** that are paid to each waitstaff for the 6-hour shift that they work, appears in the following table. 

  Time slot              minimum required             wages for 6-hour shift **

                 6am – 8am                           2                                              $70

                8am – 10am                         4                                              $60

             10am – noon                           7                                              $75

noon – 2pm                          9                                              $70

2pm – 4pm                            5                                              $80

4pm – 6pm                            8                                              -----

6pm -  8pm                           6                                              -----

 

**           Each wage per shift is based on when the waitstaff starts his/her shift.  For example, the $70 listed for the 6am – 8am time slot is the wages for those starting at 6am, and, the $60 listed for the 8am – 10am time slot is the wages for those starting at 8am, etc., etc.

 

Note:      No shifts start at 4pm or 6pm because they would not be able to work a full 6-hour shift

 

Using X1, X2, …, X5, to represent the number of waitstaff starting at 6am, 8am, … , 4pm, formulate what is being asked for so that the owner can minimize her daily wages while satisfying all her minimum requirements.  No ‘…’s are to be used anywhere in your formulations.

 

  1. the objective function

 

 

 

  1. the constraint for the 6am – 8am time slot

 

 

 

  1. the constraint for the noon – 2pm time slot

 

 

 

  1. the constraint for the 4pm – 6pm time slot

 

 

 

  1. the constraint for the 6pm – 8pm time slot
Expert Solution
steps

Step by step

Solved in 6 steps

Blurred answer
Knowledge Booster
Discrete Probability Distributions
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.
Similar questions
Recommended textbooks for you
MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman