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Heterogeneous wireless sensor networks use more than one type of nodes to improve network lifetime and scalability. In this paper, we focus on the design of a random network consisting of two types of nodes: ordinary ones and powerful ones. Ordinary nodes transmit their sensed information through powerful nodes to the data sink while powerful nodes are able to directly communicate to the sink. First, a joint lifetime-coverage analysis is presented which studies the effect of random sensors' locations on the lifetime and coverage. Then, the optimal number of each type of nodes that minimizes the network cost, while guaranteeing a desired coverage during a given time period, is found.