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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
,α
2
≥
0. Grading:

2pts points if the conditions on
α
= (
α
1
,α
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
,α
1
,α
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 nonnegativity 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 78 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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 Spring '10
 TROTTER

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