Formulate a linear programming problem to minimize the end to end delay (write the decision variable and the constraints )for the following:

Given a wireless network path that is composed of M hops. At each hop, one channel out of N channels can be used. N>M. Each of the M nodes over the path can send bi of the time. But can receive all the time, where the nodes are full duplex (i.e., can send and receive at the same time). Each of the N channels have different channel conditions if used at each hop. For example, if channel j is used at hop i, it can have a bandwidth equal Cij. Where Cij < C which is the full capacity of each channel under ideal conditions. At each hop, one channel only can be used to transmit. Each channel can be used at one hop at most. If the message M is sent at the full link capacity and the node is transmitting for the whole time, it needs time T seconds. But node i to send at channel j the message M, it needs time = T/(Cij*bi)