A storage heater captures heat over a period of time, and then releases it, usually to an air stream, when required. Those for domestic heating store solar energy or energy from cheap off-peak electricity and release it slowly during the cold part of the day. What is a good material for the core of a compact storage material capable of temperatures up to \(80^{\circ} \mathrm{C}\) and a defined storage capacity? Interpret 'compact' to mean 'of minimum volume'.

a. List the function, constraints, objective and free variable.

b. Derive a material index for selecting the material for the heat storage material.