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Unformatted text preview: one, and the total revenue
generated by the optimal solution. Also, give the average price per unit for each activity level, i.e.,
the ratio of the revenue associated with an activity, to the activity level. (These numbers should
13 be between the basic and discounted prices for each activity.) Give a very brief story explaining,
or at least commenting on, the solution you ﬁnd.
3.5 Minimizing the ratio of convex and concave piecewiselinear functions. We consider the problem
minimize maxi=1,...,m (aT x + bi )
i
mini=1,...,p (cT x + di )
i subject to F x g, with variable x ∈ Rn . We assume that cT x + di > 0 and maxi=1,...,m (aT x + bi ) ≥ 0 for all x satisfying
i
i
F x g , and that the feasible set is nonempty and bounded. This problem is quasiconvex, and can
be solved using bisection, with each iteration involving a feasibility LP. Show how the problem can
be solved by solving one LP, using a trick similar to one described in §4.3.2.
3.6 Two problems involving two norms. We consider the problem
minimize Ax − b 1
,
1− x...
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This note was uploaded on 09/10/2013 for the course C 231 taught by Professor F.borrelli during the Fall '13 term at University of California, Berkeley.
 Fall '13
 F.Borrelli
 The Aeneid

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