Consider the standard-form posynomial geometric program min 3>1x1 + x1x2 + 10> 1x323 s.t. 0.5x1x2> 1x322 … 1 0.167x1 + 0.251x120.4x2 + 0.0833x3 … 1 x1, x2, x3 7 0

(a) Change variables to convert this geometric program into a convex program.

(b) Use class optimization software to solve your convex program of part

(a) and transform optimal variable values back to obtain an optimal solution for the original NLP.

(c) Form the geometric programming dual of the original NLP.

(d) Determine the degree of difficulty of the original NLP.

(e) Use class optimization software to solve the dual of part

(c) and retrieve an optimal primal solution from the corresponding Lagrange multipliers.