The total cost of production is equal to the labor costs (a function of the weld dimensions) plus the cost of the weld and beam material.

The beam is to be optimized for minimum cost by varying the weld and member dimensions x1, x2, x3 and x4. The constraints include limits on the shear stress, bending stress, buckling load and end deflection. The variables x1 and x2 are usually integer multiples of 0.0625 inch, but for this application are assumed continuous.