In the last two exercises the objective has been that of minimizing weight. There are many others. In the selection of a material for a spring, the objective is that of maximizing the elastic energy it can store. In seeking materials for thermal-efficient insulation for a furnace, the best are those with the lowest thermal conductivity and heat capacity. However, most common of all is the wish to minimize cost. So here is an example involving cost.

Function Constraints Objective Free variables Cylindrical column Length L is specified Column must support a compressive load F without buckling Minimize the material cost of the column Cross-section area, A Choice of material