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.

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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