Consider a cantilevered steel beam of arbitrary profile exposed to a transverse force F at the tip as shown in Figure 1

Consider a cantilevered steel beam of arbitrary profile exposed to a transverse force F at the tip as shown in Figure 1. The cross-section of the beam is rectangular. 

E, 1(x) 
x = 0 
L 
Figure 1: Schematic of the beam. 

If the length of the beam is 1 m, the width is 5 cm, and the maximum weight is of the beam is 200 N, determine the (optimum) profile so that the deflection at the tip is minimized. 
Use the finite element method to determine the beam deflection. The applied force will not effect the op-timum profile; therefore, chose a force so that the deflections are reasonable. Also, the weight of the beam can be considered to have little effect on the deflection, although this assumption should he checked. 
Communicate your results in a memo which should include graphs and/or tables of the results. Place any supporting calculations and your computer code in an appendix. 
Assignment 
Specifically 1. Give a little background and description of the problem. 2. Explain the mathematical model, including all assumptions. 3. Clearly state all inputs to your model and all outputs, 4. Determine the deflection of the beam at the tip. 5. Present sufficient data (in graphical and tabular form?) and discuss your results cant factors that you considered. Communicate your results in a brief memo. A schematic, table, and/or figure will be useful to present your results. Attach all relevant calculations, programs, or spreadsheets in an appendix. Include references, properly formated.