Homework 1

Homework 1 - you found the vectors. (2) Consider a 3 n...

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CO350 LINEAR OPTIMIZATION Due Date: Friday January 12th at the beginning of class. Please do NOT leave the assignments in the drop off box but return them to the instructor in class. Important: Read the syllabus in details, particularly policies pertaining to class attendance, INC and cheating. From the notes: exercise 1.6.1. Exercise 1. You are given numbers a 1 ,a 2 ,...,a k . Write a linear program such that the optimal value of the linear program is equal to the maximum value among numbers a 1 ,a 2 ,...,a k . Exercise 2. (1) Consider the following matrix M , 1 3 - 2 2 - 1 6 - 1 2 - 3 0 1 3 4 3 1 - 1 0 2 Find a maximum number of linearly independent columns of M . Justify your answer, explain how
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Unformatted text preview: you found the vectors. (2) Consider a 3 n matrix M . Prove or disprove the following statement: M has at most 3 linearly independent columns. To prove a statement you have to provide a proof. To disprove a statement it is sufcient to exhibit a counterexample. Exercise 3. Consider the following linear program: max-x 1 + x 2 s.t. x 1 + x 2 + x 3 1 2 x 1-x 2 + x 3 = 1 x 1 , x 2 , x 3 (1) Show that no feasible solution has an optimal value greater than . (2) Find an optimal solution, and prove that it is indeed optimal. 1...
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