depot as position $0,$ suppose you have decided which customer you$$ll visit in each of the even stops on the route. To make things simple, we say customer $2$ is second, $4$ is fourth, and so on$.$ However, you can choose where in the tour you$$ll place each of the odd$-$labeled customers. In other words, you have a partial tour that looks like

$(0,?,2,?,4,?,...,0).$

For example, for n $=5,$ it would be $(0,?,2,?,4,?,0).$ If the number n of customers is even then the partial tour ends with $(...,$ n$,0),$ otherwise it ends with $(...,$ n$1,?,0).$ You want to choose positions for the odd$-$labeled customers to complete the partial tour at minimum cost. Formulate this problem as a minimum cost network flow. Clearly explain your node set, arc set, and network parameters, and justify your answer.