Linear Programming model is following:
Let
Xi = 1, if a regional manager is placed in county i, otherwise Xi = 0
Min 4830X1+8950X2+5980X3+7200X4+5970X5+8860X6+9980X7+7440X8+6990X9+7460X10+5570X11+7580X12+5170X13+5370X14+7130X15+6900X16+9500X17+5530X18+9200X19+6460X20+7130X21+8660X22+6800X23+5390X24+4940X25
s.t.
X1+X2+X6>=1
X1+X2+X3+X6+X7+X8>=1
X2+X3+X4+X8>=1
X3+X4+X5+X10+X11>=1
X4+X5+X12+X13>=1
X1+X2+X6+X7+X14+X15>=1
X2+X6+X7+X8+X9+X15+X16+X21+X22>=1
X2+X3+X7+X8+X9>=1
X7+X8+X9+X10+X16+X17>=1
X4+X9+X10+X11+X17+X18>=1
X4+X10+X11+X12+X18>=1
X5+X11+X12+X13+X19+X20>=1
X5+X12+X13+X20>=1
X6+X14+X15+X21>=1
X6+X7+X14+X15+X21>=1
X7+X9+X16+X17+X22>=1
X9+X10+X16+X17+X18+X19+X22+X23>=1
X10+X11+X17+X18+X19>=1
X12+X17+X18+X19+X20+X23+X24+X25>=1
X12+X13+X19+X20+X25>=1
X7+X14+X15+X21+X22>=1
X7+X16+X17+X21+X22+X23=1
X17+X19+X22+X23+X24>=1
X19+X23+X24+X25>=1
X19+X20+X24+X25>=1
Xi binary
--------------
Create Spreadsheet model as follows:
FORMULAS:
AA3 =SUMPRODUCT(B3:Z3,$B$31:$Z$31) copy to AA5:AA29
Enter Solver parameters:
Click Solve to generate the optimal solution:
Optimal solution:
X2=1,
X11=1
X13=1
X14=1
X16=1
X24=1
Regional manger should be placed in counties: 2, 11, 13, 14, 16, and 24
Total cost = 37,350
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