We study the problem of optimal sequential (“as-you-go”) deployment of wireless relay nodes, as a person walks along a line of random length (with a known distribution). The objective is to create an impromptu multihop wireless network for connecting a packet source to be placed at the end of the line with a sink node located at the starting point, to operate in the light traffic regime. In walking from the sink towards the source, at every step, measurements yield the transmit powers required to establish links to one or more previously placed nodes. Based on these measurements, at every step, a decision is made to place a relay node, the overall system objective being to minimize a linear combination of the expected sum power (or the expected maximum power) required to deliver a packet from the source to the sink node and the expected number of relay nodes deployed. For each of these two objectives, two different relay selection strategies are considered: (i) each relay communicates with the sink via its immediate previous relay, (ii) the communication path can skip some of the deployed relays. With appropriate modeling assumptions, we formulate each of these problems as a Markov decision process (MDP). We provide the optimal policy structures for all these cases, and provide illustrations of the policies and their performance, via numerical results, for some typical parameters.