IND ENG 160 Study Guide - Midterm Guide: Nonlinear Programming, Concave Function, Convex Function
8 Jan 2019
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Question 1 solution: let x denote the number of computers eric will buy. The nonlinear programming formulation is max 2x2 + 300x s. t. 50 x 100: the kkt condition of the problem is. 4x + 300 1 + 2 = 0. 1(100 x) = 0, 1 0. Question 2 solution: the problem can be formulated as max y2 + axy + by + c s. t. x + y = 10, the hessian of the objective function in a) is 0 a 2 . For the objective function to be a concave, its hessian must negative semidi nite. Therefore, if a = 0, b and c free, the objective function will be concave: the lagrangian function is. L(x, ) = y2 + axy + by + c + (100 x y: take the derivative of the lagrangian rpt x, y and , we get ay = 0. 2y + ax + b = 0 x + y = 10.
