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Homework 2

# Homework 2 - Math 171A Mathematical Programming Instructor...

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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. (e) Compute the residual vector r ( x ) for the constraints at the point ¯ x and find the con-

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Homework 2 - Math 171A Mathematical Programming Instructor...

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