In radiation shielding design, one is usually faced with a set of conflicting goals that are navigated by an experienced physicist. If one has abundant space, the task is simplified because concrete is relatively inexpensive and will provide adequate shielding for high energy photons and neutrons, when applicable. However, if space is constrained (which is usually the case), the design becomes more difficult since one will likely have to employ combinations of steel, lead, and concrete, or other new materials--each with different properties and costs. Very experienced shielding designers can draw upon previous plans, but they do not know if their design is optimal in any sense. We have constructed a linear program that minimizes the cost of the shielding materials and minimizes the dose at the protection point or the shielding thickness subject to space constraints and to Federal or State regulations regarding the allowable exposure to individuals adjacent to the radiotherapy vault. In spite of what appears to be a simple model, the solution may require iterations of the optimization to arrive at the optimal solution.