Chapter 3.5, Problem 5P

Explanation of Solution

Formulation of LP:

Let,

Shift 1 = 12AM‑6AM

Shift 2 = 6AM‑12PM

Shift 3 = 12PM‑ 6PM

Shift 4 = 6PM‑12AM

Let ${\text{x}}_{\text{ij}}$= workers working shifts $\text{i}$ and $\text{j}$.

The objective of the LP is to minimize the cost of meeting the daily workforce demands of the Gotham City Police Department.

Then the LP becomes,

Minimize, $z=144\left(x_{12}+x_{14}+x_{23}+x_{34}\right)+216\left(x_{13}+x_{24}\right)$

Subject to the constraints,

$\begin{array}{l}{x}_{12}+x_{13}\hfill \end{array}$