ampl: reset; model NYPD.mod.txt; data NYPD.dat.txt;
ampl: expand Total_Cost, Meet_Demand;
minimize Total_Cost:
	120*x[1,2] + 144*x[1,3] + 144*x[1,4] + 144*x[1,5] + 144*x[1,6] + 
	120*x[2,3] + 144*x[2,4] + 144*x[2,5] + 144*x[2,6] + 120*x[3,4] + 
	144*x[3,5] + 144*x[3,6] + 120*x[4,5] + 144*x[4,6] + 120*x[5,6];

subject to Meet_Demand[1]:
	x[1,2] + x[1,3] + x[1,4] + x[1,5] + x[1,6] >= 8;

subject to Meet_Demand[2]:
	x[1,2] + x[2,3] + x[2,4] + x[2,5] + x[2,6] >= 7;

subject to Meet_Demand[3]:
	x[1,3] + x[2,3] + x[3,4] + x[3,5] + x[3,6] >= 12;

subject to Meet_Demand[4]:
	x[1,4] + x[2,4] + x[3,4] + x[4,5] + x[4,6] >= 9;

subject to Meet_Demand[5]:
	x[1,5] + x[2,5] + x[3,5] + x[4,5] + x[5,6] >= 6;

subject to Meet_Demand[6]:
	x[1,6] + x[2,6] + x[3,6] + x[4,6] + x[5,6] >= 10;

ampl: solve;
Gurobi 10.0.0: optimal solution; objective 3216
7 simplex iterations
ampl: for {i in 1..n_Shift, j in i+1..n_Shift} { if x[i,j] > 0 then printf "%d, %d :   %2d\n",i,j,x[i,j];};
1, 2 :    7
1, 6 :    1
3, 4 :    9
3, 6 :    3
5, 6 :    6

# Interpretation:
# The minimum total cost to NYPD for staffing the cops is $3216. The
# numbers of cops working shifts i,j in the optimal schedule are
# listed above.