In Problem 1-8, if necessary, review Theorem 1. In Problems 1-4, the feasible region is the set of points on and inside the rectangle with vertices 0 , 0 , 12 , 0 , 0 , 5 , and 12 , 5 . Find the maximum and minimum values of the objective function Q over the feasible region. Q = 7 x + 14 y
In Problem 1-8, if necessary, review Theorem 1. In Problems 1-4, the feasible region is the set of points on and inside the rectangle with vertices 0 , 0 , 12 , 0 , 0 , 5 , and 12 , 5 . Find the maximum and minimum values of the objective function Q over the feasible region. Q = 7 x + 14 y
Solution Summary: The author calculates the maximum and minimum values of the objective function Q=7x+14y over the feasible region, based on the Fundamental Theorem of Linear Programming.
In Problem 1-8, if necessary, review Theorem 1. In Problems 1-4, the feasible region is the set of points on and inside the rectangle with vertices
0
,
0
,
12
,
0
,
0
,
5
, and
12
,
5
. Find the maximum and minimum values of the objective function
Q
over the feasible region.
Give an example of a graph with at least 3 vertices that has exactly 2 automorphisms(one of which is necessarily the identity automorphism). Prove that your example iscorrect.
3. [10 marks]
Let Go (Vo, Eo) and G₁
=
(V1, E1) be two graphs that
⚫ have at least 2 vertices each,
⚫are disjoint (i.e., Von V₁ = 0),
⚫ and are both Eulerian.
Consider connecting Go and G₁ by adding a set of new edges F, where each new edge
has one end in Vo and the other end in V₁.
(a) Is it possible to add a set of edges F of the form (x, y) with x € Vo and y = V₁ so
that the resulting graph (VUV₁, Eo UE₁ UF) is Eulerian?
(b) If so, what is the size of the smallest possible F?
Prove that your answers are correct.
Let T be a tree. Prove that if T has a vertex of degree k, then T has at least k leaves.
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