Population estimated for the Late Classic period at the Lowland Maya site of Tikal, Guatemala, is reviewed. Linear programming is described and suggested as a method for simulating the agricultural carrying capacity of the sustaining area of the site, thereby inferring its potential population. Archaeological data on the estimated size of the Tikal sustaining area is presented along with modern agricultural production and caloric output figures for maize, root crops, and ramon seeds. These data are used in the computation of a linear program. The results of the computer runs calculating the maximum population supportable by different combinations of milpa, intensive farming, and aboriculture are discussed. These results suggest that a mixed subsistence strategy in which ramon seed aboriculture and intensive root cropping were combined and were supplemented by kitchen gardening, hunting, gathering, and trade might have supported a population as high as 69,705 to 76,699 people within the boundaries of the site of Tikal during the Late Classic period.