The advent of Machine-to-Machine communication has sparked a new wave of interest to random access protocols, especially in application to LTE Random Access (RA). By analogy with classical slotted ALOHA, state-of-the-art models LTE RA as a multi-channel slotted ALOHA. In this letter, we direct the attention to the resource consumption of RA. We show that the consumption is a random variable dependent on the contention parameters. We consider two approaches to include the consumption into RA optimization: by defining resource efficiency and by the means of a bi-objective optimization, where resource consumption and throughput are the competing objectives. We then develop the algorithm to obtain Pareto-optimal RA configuration under resource constraint. We show that the algorithm achieves lower burst resolution delay and higher throughput than the state-of-the-art.