A Randomly Weighted Minimum Spanning Tree with a Random Cost Constraint

We study the minimum spanning tree problem on complete graph $K_n$ where an edge $e$ has a weight $W_e$ and cost $C_e$, each of which is independent copy random variable $U^\gamma$ $\gamma\leq 1$ $U$ uniform $[0,1]$ variable. There also constraint that $T$ must satisfy $C(T)\leq c_0$. establish, for range values $c_0,\gamma$, asymptotic value optimum via consideration dual problem.