MATH373 Midterm: MATH 373 UofA Midterm 2
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@ualberta. ca: scrap paper is supplied, no notes or books are permitted, all electronic equipment, including calculators, is prohibited. Make certain that cell phones are turned o . Check that you have 5 pages: this exam consists of 3 questions, for a total of 20 points. If anything is unclear, please ask: use theorem 2. 7 to establish that the system of inequalities x1 2x2 2, 2x1 +3x2 1 has no non-negative solutions. Note that the corresponding set of constraint vectors {(1, 2), (2, 3), (1, 0), (0, 1)} con- tains 2 linearly independent vectors (for example the third and fourth vectors are ac- tually orthogonal). Theorem 2. 7 then tells us that if p is nonempty, it must contain at least one extreme point. We are asked to show that p is empty, so all we really need to show is that p contains no extreme points (basic feasible solutions).
