Minimizing the amount of time and number of processors needed to perform an application reduces the application's fabrication cost and operation costs. A directed acyclic graph (dag) model of algorithms is used to define a time-minimal schedule and a processor-time-minimal schedule, We present a technique for finding a lower bound on the number ofprocessorsneeded to achieve a given schedule of an algorithm. The application of this technique is illustrated with a tensor product computation. We then apply the technique to the free schedule of algorithms for matrix product, Gaussian elimination, and transitive closure. For each, we provide a time-minimal processor schedule that meets these processor lower bounds, including the one for tensor product.