(Urgent) linear programing modeling (Operation Research)

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20C992

Engineering

Description

Please check the attachment before bidding. (No late submissions please)

  • Please read the question carefully and understand what's been asked well.
  • Correctly model the problem as a linear program. You must show the mathematical model. You must declare your decision variables, objective function, and constraints. Your solution must be written out completely and logically.
  • Solve your linear program using the IBM ILOG CPLEX Optimization Studio.You must attach the actual CPLEX file as well as the solution in a word doc. You also need to attach a screenshot of your code along with a screenshot of the solution.

You have 2 days to finish this while you don't need all this time, So please submit the work the earliest.

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Lafene Health Center Workforce Scheduling Lafene Health Center is planning to open its facilities 24 hours a day and wants to determine an optimal schedule for their nurses. A nurse's work schedule is 8 hours in a row and can only start at the beginning of each shift. The personnel requirement for each shift is shown in Table 1. Table 1 - Personnel Requirement Shift Time Required Nurses 1 8:00am-12:00pm 50 2 12:00pm-4:00pm 56 3 4:00pm-8:00pm 60 4 8:00pm-12:00am 42 5 12:00am-4:00am 32 6 4:00am-8:00 am 24 Each nurse is paid $100 per hour in the daytime (from 8:00am to 8:00 pm) and $125 at night (from 8:00pm to 8:00am on the following day). Consider that each nurse can also work overtime hours. If a nurse works overtime hours, then she/he will work 4 consecutive hours beyond her/his normal work time, and be paid an additional 50% for each of the 4 hours. Furthermore, no more than 25% of the nurses can work overtime hours at each shift. Formulate a linear program to minimize labor expenses. You must solve the linear program using the IBM ILOG CPLEX Optimization Studio. (Hint: If your solution is correct, it will provide integer values)
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