{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

math171a_hw2_sol

math171a_hw2_sol - Math 171A Homework 2 Solutions...

Info icon This preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
Math 171A Homework 2 Solutions Instructor: Jiawang Nie February 1, 2012 1. (8 points) Consider the feasible set F defined by the following constraints x 1 + x 2 4 , x 1 + 3 x 2 6 , 6 x 1 - x 2 18 , 3 x 2 6 , x 1 ≥ - 1 . (a) Express F in the standard form Ax b . Write down A and b explicitly. Solution: A = 1 1 1 3 - 6 1 0 1 0 - 1 1 0 b = 4 6 - 18 3 - 6 - 1 (b) Draw the set F graphically in the plane, and find all the corner points of F . Solution: Like the previous homework, we draw all of the lines and find which side of the lines the feasible region is on, see Figure 1. Then by finding which lines intersect we can solve for the corners. The corners that lie in the feasible region should be ( - 1 , 5) , (1 , 3) , (3 . 5 , 3) , (4 , 6) , ( - 1 , 6) (c) Solve the following LP minimize 2 x 1 - 3 x 2 subject to Ax b where A and b are from part (a). Solution: Since we know the corner points of the feasible region from part (b), we need to plug those points into the objective function and compare. At five corner points, the objective function values are -17, -7, -2, -10, -20 respectively. The point which minimizes 2 x 1 - 3 x 2 is the point ( - 1 , 6) with a value of - 20. 1
Image of page 1

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
-1 0 1 2 3 4 5 6 -25 -20 -15 -10 -5 0 5 10 15 20 C6 Feasible Region C5 C4 C3 C2 C1 Figure 1: Feasible Region of Question 1. (d) Compute the residual vector r ( x ) for all the constraints at the point ¯ x = (2 , 4), and find the constraints whose residuals would decrease after a positive step α
Image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern