
Concept explainers
Explanation of Solution
Formulation of LP:
Let,
The objective is to minimize the number of police officer’s needed to meet daily requirements.
That is,
Objective function:
Minimize,
Now, the requirement of number of on-duty police officers during midnights 12 to 4 am is 8 and each police officer work two consecutive 4-hours shift.
Therefore, the constraints will be,
Similarly the requirement of number of on-duty police officers during 4 am to 8 am is 7 second constraint is,
Requirement of number of on-duty police officer’s during 8 am to 12 noon is 6,
Requirement of number of on-duty police officers during 12 noon to 4 pm is 6.
Requirement of number of on-duty police officer’s during 4 pm to 8 pm is 5.
Requirement of number of on-duty police officer’s during 8 pm to 12 midnight is 4.

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Chapter 3 Solutions
Introduction to mathematical programming
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