hw5 - Math 171A: Linear Programming Instructor: Philip E....

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Math 171A: Linear Programming Instructor: Philip E. Gill Winter Quarter 2011 Homework Assignment #5 Due Friday February 11, 2011 Starred exercises require the use of Matlab . Exercise 5.1. * Consider the set of inequality constraints Ax b , where A = 1 1 0 1 1 3 0 1 1 0 6 1 and b = 4 3 6 6 1 18 . (a) Given the point ¯ x = (5 2 ) T and the direction p = ( 1 1 ) T , ±nd the step σ i along p to each constraint a T i x b i . For each constraint, determine if ¯ x is feasible and state if a positive step moves towards the feasible half-space or away from the feasible half-space. (b) Given the feasible point ¯ x = (2 4 ) T and direction p = ( 1 1 ) T , determine the constraints active at ¯ x and compute the maximum positive feasible step that can be taken along p .
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hw5 - Math 171A: Linear Programming Instructor: Philip E....

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