An inventive method was applied to determine the minimum major radius, R0, and the optimum build of a tokamak fusion reactor that simultaneously meets all physics, engineering, and neutronics constraints. With a simple cost model, tokamak systems analyses were carried out over ranges of system parameters to find an optimum build of a tokamak fusion reactor at minimum cost. The impact of a wide range of physics parameters and advanced engineering elements on costs were also addressed. When a central solenoid was used to ramp up a plasma current, design solutions with a cost of electricity (COE) between 109 and 140 mills/kWh, direct capital cost between 5000 and 6000 M/USD, and net electric power, Pe between 1000 and 1600 MW could be found with a minimum R0 between 6.0 and 7.0 m, and fusion power, Pfusion between 2000 and 2800 MW. When the plasma current was driven by a non-inductive external system, the system size and costs could be reduced further; a COE between 98 and 130 mills/kWh, direct capital cost between 4000 and 5000 M$, and Pe between 1000 and 1420 MW could be found with a minimum R0 between 5.1 and 6.7 m, and Pfusion between 2000 and 2650 MW.