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In this paper, we examine the resource optimization problem in a broadcast relay network where a source broadcasts signals to the user receivers, which are distributed over a service region. The source does not have direct line-of-sight to the service area and the information is delivered through a relay. The objective of this paper is to jointly optimize the relay position as well as the power allocation between the source and relay so that the outage probability of the signal received at the user nodes is minimized. Two different optimization criteria, which respectively minimize the worst-case outage probability and the average outage probability, are used. The analyses are verified by simulation results.