In Problems 13-20, write the e-system obtained via slack variables for the given linear programming problem. Maximize P = 3 x 1 + 5 x 2 subject to 12 x 1 − 14 x 2 ≤ 55 19 x 1 + 5 x 2 ≤ 40 − 8 x 1 + 11 x 2 ≤ 64 x 1 , x 2 ≥ 0
In Problems 13-20, write the e-system obtained via slack variables for the given linear programming problem. Maximize P = 3 x 1 + 5 x 2 subject to 12 x 1 − 14 x 2 ≤ 55 19 x 1 + 5 x 2 ≤ 40 − 8 x 1 + 11 x 2 ≤ 64 x 1 , x 2 ≥ 0
Solution Summary: The author explains the e-system using the slack variable for maximizing P=3x_1+5
12:25 AM Sun Dec 22
uestion 6- Week 8: QuX
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Assume that a company is considering purchasing a machine for $50,000 that will have a five-year useful life and a $5,000 salvage value. The
machine will lower operating costs by $17,000 per year. The company's required rate of return is 15%. The net present value of this investment
is closest to:
Click here to view Exhibit 12B-1 and Exhibit 12B-2, to determine the appropriate discount factor(s) using the tables provided.
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$6,984.
$11,859.
$22,919.
○ $9,469,
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7. [10 marks]
Let G
=
(V,E) be a 3-connected graph. We prove that for every x, y, z Є V, there is a
cycle in G on which x, y, and z all lie.
(a) First prove that there are two internally disjoint xy-paths Po and P₁.
(b) If z is on either Po or P₁, then combining Po and P₁ produces a cycle on which
x, y, and z all lie. So assume that z is not on Po and not on P₁. Now prove that
there are three paths Qo, Q1, and Q2 such that:
⚫each Qi starts at z;
• each Qi ends at a vertex w; that is on Po or on P₁, where wo, w₁, and w₂ are
distinct;
the paths Qo, Q1, Q2 are disjoint from each other (except at the start vertex
2) and are disjoint from the paths Po and P₁ (except at the end vertices wo,
W1, and w₂).
(c) Use paths Po, P₁, Qo, Q1, and Q2 to prove that there is a cycle on which x, y, and
z all lie. (To do this, notice that two of the w; must be on the same Pj.)
Elementary Statistics: Picturing the World (7th Edition)
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