prelim1Q2_rough_grading_guide - Prelim 1 Problem 2 rough...

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Prelim 1 Problem 2 – rough grading guide (a) Correct condition: 4 - α 1 π 1 - α 2 π 2 > 0 for some α 1 , α 2 such that 2 α 1 + 3 α 2 = 4 and α 1 2 0. Grading: - 2pts points if the conditions on α = ( α 1 2 ) were missing; - 1pt if the inequality was not strict. (b) LP sufficient for full credit: max { 4 - π 1 α 1 - π 2 α 2 : 2 α 1 +3 α 2 = 4 1 2 0 } – although strictly speaking, constant 4 should not be part of the objective. Grading: • - 3pts if the objective was incorrectly multiplied by x 3 ; • - 1pt if the non-negativity constraint was missing; • - 4pts if the objective was minimized instead of maximized; Maximum 2pts if the LP was totally wrong (that is, both objective and constraints involving mainly x ’s) but also involved the two “correct” constraints on α . Too many special cases to discuss, but as a general rule, any “partially correct” LP involving (nec- essarily incorrect) constraints on x could not get more than 7-8 points due to significance of the mistake. (c) General comment: Most of you have not realized that the problem given here
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