For a rectangular prism, determine the dimensions b, h for the least mass under the following conditions:
- The deflection (the most that the prism can bend) cannot exceed 50mm.
- Height h cannot be greater than b.
- E = modulus of elasticity 2.0 x 10^11Pa
- L = length of beam 6.0 meters
- P = 1.0 x 10^5 N
- d = (PL^3) / 3EI
- I = moment of inertia, m^4
- for rectangular cross section; I = (bh^3)/12

Question

For a rectangular prism, determine the dimensions b, h for the least mass under the following conditions:
- The deflection (the most that the prism can bend) cannot exceed 50mm.
- Height h cannot be greater than b.
- E = modulus of elasticity 2.0 x 10^11Pa
- L = length of beam 6.0 meters
- P = 1.0 x 10^5 N
- d = (PL^3) / 3EI
- I = moment of inertia, m^4
- for rectangular cross section; I = (bh^3)/12