Design problem: For a 4 meter length beam loaded at the end by a force of 100kN, find the size of beam that minimizes the cost (i.e. volume) while meeting the following constraints--

a) d 40 mm

b) h 3b

where d is the deflection, h is the height, and b is the width.

Beams come in multiples of 50 mm (Thus, a 50 mm X 50 mm beam is available, or a 50 mm X 100 mm beam is available, etc).

The deflection is given by the following expression: d=(4PL^3)/(Ebh^3), where P is the applied force (100kN), L is the length, and E is the elastic modulus of the material and is equal to 200 GN/m^2.