The influence of design variations, such as the percentage of structural material in a tritium breeding zone or the enrichment of lithium in 6Li, on such important controlled thermonuclear reactor parameters as the tritium breeding ratio and the total nuclear energy produced has been studied using variational techniques for two different but general blanket designs. The first design uses liquid lithium as both coolant and breeding material, while the second uses a helium coolant and a solid-lithium-bearing compound as the tritium breeder. A variational technique based on variational interpolation is the primary computational tool, and it is shown that for linear perturbations in the transport operator and for a fixed source, only forward flux calculations are required to implement the variational interpolation approach. No adjoint functions are required, while any number of response functionals can be investigated. For both blanket designs, the influence of the choice of structural material, such as stainless-steel, molybdenum, niobium, vanadium, and aluminum structures, has been studied. The role of beryllium as a neutron multiplier with a solid breeder blanket is studied, and an optimum beryllium thickness is found that maximizes the breeding ratio. The influence of using graphite or the structural material as a neutron reflector and the effect of lithium burnup are also studied. It is found that for a given percentage of structural material in the tritium breeding zones, vanadium-structured systems achieve the highest breeding ratios, while molybdenum-structured systems produce the highest value of total nuclear heating. The effects of lithium burnup are small.