A network flow method is outlined for solving the linear programming problem of computing the least cost curve for a project composed of many individual jobs, where it is assumed that certain jobs must be finished before others can be started. Each job has an associated crash completion time and normal completion time, and the cost of doing the job varies linearly between these extreme times. Given that the entire project must be completed in a prescribed time interval, it is desired to find job times that minimize the total project cost. The~method solves this problem for all feasible time intervals.