Min Problem min z = -2x 1 -3x 2 s.t x 1 - x 2 <= 1 - x 1 - 2x 2 <= 2 x 1 , x 2 >=0

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QUESTION 9 What is one advantage of AABB over Bounding Spheres? Computing the optimal AABB for a set of points is easy to program and can be run in linear time. Computing the optimal bounding sphere is a much more difficult problem. The volume of AABB can be an integer, while the volume of a Bounding Sphere is always irrational. An AABB can surround a Bounding Sphere, while a Bounding Sphere cannot surround an AABB. To draw a Bounding Ball you need calculus knowledge.

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Chapter 4.8, Problem 2P

Program Plan Intro

Min Problem

min z = -2x₁-3x₂

s.t x₁ - x₂ <= 1

_-x₁ - 2x₂ <= 2

x₁, x₂>=0

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QUESTION 9 What is one advantage of AABB over Bounding Spheres? Computing the optimal AABB for a set of points is easy to program and can be run in linear time. Computing the optimal bounding sphere is a much more difficult problem. The volume of AABB can be an integer, while the volume of a Bounding Sphere is always irrational. An AABB can surround a Bounding Sphere, while a Bounding Sphere cannot surround an AABB. To draw a Bounding Ball you need calculus knowledge.

K = 0, L = 18 Write and solve the following linear program using lingo, take screen shots of your model as well as the reports and the optimal solution. Clearly show the optimal solution.NB:K=the second digit of your student number;L=sum of the digits of your student number, For example if your student number is 17400159 thenK=7andL=1+7+4+0+0+1+5+9=27!!!! SAVE YOUR FILE BY YOUR STUDENT NUMBER!!!!minz=t∈T∑(AtYt+PtXt)+k∈K∑(HkUk+BkVk)s.t.Uk+Vk=50∀k∈KXt−CtYt<=0∀t∈Tk∈K∑Vk≥80t∈T∑Xt≥t∈T∑DtXt>=0∀t∈TYt∈{0,1}∀t∈TUk>=0∀k∈KVk>=0∀k∈KThe sets parameters and data are as follows: \[ \begin{array}{l} \mathrm{T}=\{1,2,3,4\} \\ \mathrm{K}=\{0,1,2,3,4\} \\ \mathrm{A}=\{5000,7000,8000,4000\} \\ \mathrm{D}=\{250,65,500,400\} \\ \mathrm{C}=\{500,900,700,800\} \\ \mathrm{P}=\{20, \mathrm{~L}, 25,20\} \\ \mathrm{H}=\{5,3,2, \mathrm{~K}, 9\} \\ \mathrm{B}=\{8,5,4,7,6\} \end{array} \]

A circus is planning a tower act in which individuals stand on top of one another's shoulders. Each individual must be both shorter and lighter than the person below him or her for practical and aesthetic reasons. Write a way to determine the maximum feasible number of people in such a tower given the heights and weights of each individual in the circus.