Thanks a lot Ian. Your post helped me understand the problem in a much better 
way and I've solved the first objective thanks to you but incase of my second 
objective which is minimize the number of nodes, I have got one of the weirdest 
looking constraints which I don't know how to express in Python because python 
basically takes matrices and inputs them into cplex. My constraint is as below. 
Thsi was what I wrote in AMPL

minimize phy_nodes: sum {w in PHY_NODES} x_ns[w] ;

s.t. Phy_nodes_Eq{w in PHY_NODES, dns in DEMAND}: 
x_ns[w] = 1 ==> x_SGW[dns, w] + x_PGW[dns, w] + x_MME[dns, w] + x_IMS[dns, w] + 
x_PoP[dns, w] >= 1 
else x_SGW[dns, w] + x_PGW[dns, w] + x_MME[dns, w] + x_IMS[dns, w] + x_PoP[dns, 
w] = 0;
Could you help me fix this problem?
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