In this paper, we study the problem of aggregate utility maximization in multihop wireless networks. Following standard approaches, we consider the dual of a convex optimization problem that can be decomposed into two sub-problems. One of the sub-problem is a scheduling problem that requires enumeration of all maximal independent sets in the network—a well-known NP-hard problem. To overcome this computational complexity, we resort to polynomial-time sub-optimal Greedy Maximal Scheduling (GMS). The majority of this paper is dedicated towards quantifying the sub-optimality that arises in the aggregate utility maximization problem due to GMS. We also provide some insights into factors affecting aggregate utility maximization by providing bounds on the maximum achievable aggregate utility.