This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.View Full Document
Unformatted text preview: Math 171A: Mathematical Programming Instructor: Philip E. Gill Winter Quarter 2009 Homework Assignment #2 Due Friday January 23, 2009 The starred exercises require the use of Matlab . Remember that it is necessary to do all the Matlab assignments to obtain credit for the class. Exercise 2.1. (a) Write the constraints x 1 + x 2 4, x 1 + 3 x 2 6, 6 x 1- x 2 18, 3 x 2 6 and x 1 - 1 in matrix form Ax b . (b) Draw the graphical representation of the feasible region defined by the constraints of part (a) . Mark the infeasible side of the half-space defined by each constraint. (c) Consider the linear function ( x ) = c T x where c T = ( 2- 3 ). On your graph from part (a) , show the halfspace of descent directions emanating from the point x = (2 , 4). (d) Use the graphical method to minimize 2 x 1- 3 x 2 subject to the constraints of part (a) . Give the optimal values of x 1 , x 2 and the minimum value of the objective function....
View Full Document