In this paper, a novel method is proposed to dimension a randomly deployed heterogeneous Wireless Sensor Network (WSN) of minimum monetary cost satisfying minimum coverage and minimum lifetime requirements. We consider WSNs consisting of two different types of nodes clusterheads and ordinary sensor nodes, randomly deployed over a sensing field. All devices are assumed to be stationary and have identical sensing capabilities. However, the clusterheads are more energetic and powerful in terms of processing and communication capabilities compared to sensor nodes. For such a network, finding minimum cost WSN problem is not a trivial one, since the distribution of the mixture of two different types of devices and the batteries with different initial energies in each type of device primarily determine the monetary cost of a WSN. Therefore, we formulated an optimization problem to minimize the monetary cost of a WSN for given coverage and lifetime requirements. The proposed optimization problem is solved for a certain scenario and the solution is validated by computer simulations.