The increasing resistance of harmful biological organisms (bacteria, parasites, and pests) to selection pressure from the widespread use of control agents such as antibiotics, antimalarials, and pesticides is a serious problem in both medicine and agriculture. Modeling resistance —or, conversely, the effectiveness of these control agents as a biological resource—yields insights into how these agents should be optimally managed to maximize their economic benefit to society. This paper uses a model of evolution of bacterial resistance to antibiotics—in which resistance places an evolutionary disadvantage on the resistant organism—to develop a simple sequential algorithm of optimal antibiotic use. Although the solution to this problem follows the well-recognized rule of using resources in the order of increasing marginal cost, the unique ways in which these economic costs arise from differing biological traits distinguishes this problem from others in the natural resources arena. This paper also examines the option of periodically rotating between two or more antibiotics and characterizes the economic and biological criteria under which a cycling strategy is superior to simultaneous use of two or more antibiotics.