A Police Department Is Trying to Allocate Crime Control Resources

question 101

Multiple Choice

A police department is trying to allocate crime control resources between murder and burglary.Detectives cost $40,000 each.Suppose that she marginal benefit of one less murder is $20,000 while the marginal benefit of one less burglary is $1,000.The number of murders and burglaries that occur at different levels of detective allocation is shown in the table. $\begin{array}{ccc}\begin{array}{c}\text { Number of } \\\underline { \text { Detectives Assigned }}\end{array} & \begin{array}{c}\text { Number of } \\\underline { \text { Murders }}\end{array} & \begin{array}{c}\text { Number of } \\\underline { \text { Burglaries }}\end{array} \\ 0 & 20 & 100 \\1 & 16 & 60 \\2 & 13 & 30 \\3 & 11 & 10 \\4 & 10 & 0\end{array}$
The marginal benefits of 1,2,3,and 4 detectives being assigned to murder prevention are

• A)4,3,2,and 1.
• B)$4,000,$3,000,$2,000,and $1,000.
• C)$16,000,$13,000,$11,000,and $10,000.
• D)$80,000,$60,000,$40,000,and $20,000.

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Definitions:

Objective Function

A mathematical function used in optimization that defines the goal to be achieved, often maximizing or minimizing some quantity.

Optimal Solution

The best possible outcome or answer found for a given problem, often characterized by the most efficient allocation of resources to achieve desired objectives.

Northwest-Corner Rule

A method used in transportation problems of operations research to find an initial feasible solution by starting from the top-left (northwest) corner of a matrix.

Initial Feasible Solution

The starting point of an algorithm that represents a possible solution to a problem, which meets all the constraints of the problem.