Exercise 3.22. Let n?3 and m?2 be two integers. The simple plant location polytope is the convex hull of the points (x,y)?{0,1}mn{0,1}n satisfying ?j=1n?xij?=10?xij??yj??1?i=1,,mi=1,,m,j=1,,n? (i) Find the dimension of the simple plant location polytope. (ii) Show that xij??0 defines a facet of the simple plant location polytope for a solutionspile.com

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Exercise 3.22. Let n?3 and m?2 be two integers. The simple plant location polytope is the convex hull of the points (x,y)?{0,1}mn{0,1}n satisfying ?j=1n?xij?=10?xij??yj??1?i=1,,mi=1,,m,j=1,,n? (i) Find the dimension of the simple plant location polytope. (ii) Show that xij??0 defines a facet of the simple plant location polytope for all i=1,,m and j=1,,n. (iii) Show that yj??1 defines a facet of the simple plant location polytope for all j=1,,n. (iv) Show that xij??yj? defines a facet of the simple plant location polytope for all i=1,,m and j=1,,n. solutionspile.com

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