A cantilevered beam shown in the figure is under a couple of \(500 \mathrm{lb}\). in. at the end. The optimization problem is to find a design that minimizes the crosssectional area, while the maximum stress is less than 2,000 psi. The thicknesses of the flange and the web of the cross section are fixed with \(t=0.1 \mathrm{in}\). The design variables are the width \(w\) and the height \(h\) of the cross section. Determine graphically the optimal design. The width and the height are constrained to remain in the range \(0.1 \leq w \leq 10\) in and \(0.2 \leq h \leq 10\) in.

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W - 12 h