Math 340 Note Sheet for the Final Exam, Fall 2014
ValueAliceAnnouncesPure(A) = max MinEntry of i-th row of A = max min aij
i
i
j
ValueBettyAliceAnnouncesPure(A) = min MaxEntry of j-th column of A = min max aij
j
j
i
DualityGap = (ValueBettyAnnouncesPure)
Math 340101
Fall 2014
Solutions: Homework #5
1. (a) The value is between 1 and 16 since these are the smallest and
largest entries of A.
(b)
maximize = v,
subject to
and
v + p1 + 4p2 + 9p3 + 16p4 0,
v + 16p1 + 9p2 + 4p3 + p4 0,
p1 + p2 + p 3 + p4
1
v, p1
Math 340 Note Sheet for Midterm, Fall 2014
ValueAliceAnnouncesPure(A) = max MinEntry of i-th row of A = max min aij
i
i
j
ValueBettyAliceAnnouncesPure(A) = min MinEntry of j-th column of A = min max aij
j
j
i
DualityGap = (ValueBettyAnnouncesPure) (ValueA
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