Suppose you have an algorithm A that is capable of solving the minimum

cost perfect matching problem in a complete bipartite network. Explain

how you could use this algorithm to solve the following problems:

$($a$)$ The minimum multiplicative cost perfect matching problem in a com$-$

plete bipartite network with strictly positive edge weights, in which

you seek a perfect matching that minimizes the product of the costs

of the selected edges:

$minimiz{e}_{x}pro{d}_{(i,j)\text{:}{x}_{ij}}=1c_{ij}s.t.$

${\displaystyle \underset{i=1}{\overset{n}{}}}{x}_{ij}=1$AAj

${\displaystyle \underset{j=1}{\overset{n}{}}}{x}_{ij}=1$AAi

$x_{ij}in\{0,1\}.$