Example Nonlinear Programming Problems Problem 1. (Difficulty level: 2) (1) Derive the model for a uniform column of tubular section to carry a compressive load P=2500kgr for minimum cost. The column is made up of a material that has a yield stress (cy) of 500kgg'cm?, modulus of elasticity (E) of 0.85x10%g/cm', and density (p) of 0.0025kgs/cm'. The length of the column is 250cm. The stress induced in the column should be less than the buckling stress as well as the yield stress. The mean diameter of the column is restricted to lie between 2 and 14cm, and column with thickness outside the range 0.2 to 0.8cm are not available in the market. The cost of the column includes material and construction costs and can be taken as SW+2d. where I is the weight in kgrand d is the mean diameter of the column in cm. (2) Design d and t to minimise the cost (use at least two different optimisation techniques/software to find the solution and compare the results): (3) Discuss the effects of d and t on the cost, and the other important factors: (4) Based on the solution and discussion, prepare a report which provides detailed design guideline for the column design (assuming your colleagues will use this guideline in their designs of this type of columns). L . P