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# HW7 - 7th Homework for IEOR162 Linear Programming Semester...

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7th Homework for IEOR162 Linear Programming Semester: Fall 2010 Instructor: Dr. Sarah Drewes Due to: Tuesday, November 16, 2010 (at the beginning of class) P1 Compute the inverse of the following matrix A = 1 0 2 2 1 4 0 1 1 . P2 Show that the inverse of a matrix A = ± a b c d ² is given by A - 1 = 1 ad - bc ± d - b - c a ² . P3 Suppose when solving an LP (max), we obtain the following tableau z x 1 x 2 x 3 x 4 rhs 1 -3 -2 0 0 0 0 1 -1 1 0 3 0 2 0 0 1 4 Why is this LP unbounded? P4 Consider an LP (max) with the following optimal tableau z x 1 x 2 x 3 x 4 rhs 1 0 0 0 2 2 0 1 0 -1 1 2 0 0 1 -2 3 3 Does this LP have more than one basic feasible solution that is optimal? P5 A company manufactures two types of radios. We consider here the labor hours needed to produce the radios. The company has two laborers, where laborer 1 is willing to work 40 1

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hours a week and is paid \$ 5 per hour, laborer 2 is willing to work up to 50 hours per week and is paid \$ 6 per hour. One radio of Type 1 requires 1 hour of labor of laborer 1, 2 hours
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HW7 - 7th Homework for IEOR162 Linear Programming Semester...

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