The LASREF facility is located in the beam stop area at LAMPF. The neutron spectrum is fission-like with the addition of a 3% to 5% component with E > 20 MeV. The present study evaluates the limits on geometry and material selection that will maximize the neutron flux. MCNP and LAHET were used to predict the neutron flux and energy spectrum for a variety of geometries. The problem considers 760 MeV protons incident on tungsten. The resulting neutrons are multiplied in uranium through (n,xn) reactions. Calculations show that a neutron flux greater than 10199 n/m2/s is achievable. The helium to dpa ratio and the transmutation product generation are calculated. These results are compared to expectations for the proposed DEMO fusion reactor and to FFTF.