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    Algebra - Linear Programming

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    The central police department had recently been criticized in the local media for not responding to police calls in the downtown area rapidly enough. In several recent cases, alarms had sounded for break-ins, but by the time the police car arrived, the perpetrators had left, and in one instance a store owner had been shot. Sgt Davis had been assigned by the chief as head of a task force to find a way to determine the optimal patrol area for their cars that would minimize the average time it took to respond to a call in the downtown area.

    Sgt Davis solicited help from an analyst, Ms. Maris in the operation area for the police department. Together they began to work through the problem. ...

    [See the attached question file.]

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    The central police department had recently been criticized in the local media for not responding to police calls in the downtown area rapidly enough. In several recent cases, alarms had sounded for break-ins, but by the time the police car arrived, the perpetrators had left, and in one instance a store owner had been shot. Sgt Davis had been assigned by the chief as head of a task force to find a way to determine the optimal patrol area for their cars that would minimize the average time it took to respond to a call in the downtown area.

    Sgt Davis solicited help from an analyst, Ms. Maris in the operation area for the police department. Together they began to work through the problem.

    Sgt Davis noted to Ms Maris that normal patrol sectors are laid out in rectangles, with each rectangle including a number of city blocks. For illustrative purposes he defined the dimensions of the sector as x in the horizontal direction and as y in the vertical direction. He explained to Ms Maris that cars traveled in straight lines either horizontally or vertically and ...

    Solution Summary

    The expert examines a linear programming case for the central police department. A neat and step-wise solutions are provided. Graph is shown.

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