EGM6365 Homework #2 1. Consider the following design optimization problem: 22121113321Minimize( )44Subject to( )0()0(1) 0fxxxgxx=+− +=− ≤=−≤=−− ≤xxxx(i)Find the optimum point graphically (ii)Show that the optimum point does not satisfy K-T condition. Explain 2. An engineering design problem is formulated as: Minimize 121225210xxx=+ − − +xSubject to the constraints 21122303260hx xgxx=+ −==+−≤In all of the following questions, justify your answers. (i)Write K-T necessary conditions (ii)How many cases are there to be considered? Identify those cases. (iii)Find the solution for the case where g1is active. Is this acceptable case? (iv)Regardless of the solution you obtained in (iii), suppose the Lagrange multiplier for the constraint h1= 0 is λ1= -2 and the Lagrange multiplier for the constraint
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