Mid-field (0.5T) MRI is an attractive alternative to higher field strengths for improved cost, accessibility and patient comfort. Magnet length is a major determinant of patient comfort/acceptance but is constrained by escalating wire costs. We present a mid-field magnet design using rare-earth permanent magnets to supplement solenoidal superconducting windings, enabling shorter bore lengths than superconducting windings alone. The optimization problem is formulated and solved using linear programming. For a given superconducting wire length, we demonstrate that adding rare-earth materials can reduce bore lengths by 10% using <250kg of rare-earth material for a 5ppm, 0.5T B0 specification over a 450mm DSV.