The Metro Police Department has partitioned the city into four quadrants. The department has 20 police patrol cars available for each shift per day to assign to the quadrants. The depart- ment wants to assign patrol cars to the quadrants during a shift so that the crime rate is minimized while providing average response times to calls of less than 10 minutes. As patrol cars are assigned to a quadrant, the crime rate and response time decrease, but at a decreasing rate according to the following formula:
y= a+ ( b/ x)
The aand bparameters for daily crime rate (expressed as crimes per 1,000 population) and response time (in minutes) are provided in the following table:
CrimeRate Response Time(min.)
|
Quadrant
|
a
|
b
|
|
a
|
b
|
|
1
|
0.24
|
0.15
|
|
4
|
11
|
|
2
|
0.37
|
0.21
|
|
8
|
8
|
|
3
|
0.21
|
0.12
|
|
6
|
10
|
|
4
|
0.48
|
0.30
|
|
3
|
9
|
Formulate and solve a nonlinear programming model to determine the number of police patrol cars to assign to each quadrant that will result in the minimum overall crime rate.