1. Formulate the following as an optimization problem instance, and give the domain of feasible solution and the cost function: Find a cylinder with a given surface area that has the largest volume.
2. Suppose we are given a set containing 2 integers, and we wish to partition it into two sets1 and2 so that |1 | = |2 | = and so that the sum of the numbers in1 is as close as possible to the sum of those in2. Let the neighborhood be determined by all possible interchanges of two integers between1 and2. Is exact?
3. Let() be convex in. Fix2, . . . , and consider the function(1) =(1,...,). Is g convex in 1?
4. Let() be a convex function of the single variable. Then() can also be considered as a function of. Is() convex in?
5. Show that the set of optimal points of an instance of LP is a convex set.