Let's consider the following linear inequalities: a &#x2212;<!-- − --> 10 &#x2264;<!--

antennense

antennense

Answered question

2022-07-15

Let's consider the following linear inequalities:
a 10 b a 7 b + 3 c b + 6 c + 3 d c + 6 d + 3 e d + 6
Is there a way to find a solution to this system where max ( | a | , | b | , | c | , | d | , | e | ) is minimized?

Answer & Explanation

lywiau63

lywiau63

Beginner2022-07-16Added 13 answers

With the changed question, the minimised maximum absolute value is 4.5
You have e d + 3 c + 6 b + 9 so e b 9 and max ( | b | , | e | ) 4.5
An optimal solution is ( 2.5 , 4.5 , 1.5 , 1.5 , 4.5 ) and others are similar with a [ 2.5 , 4.5 ]
dream13rxs

dream13rxs

Beginner2022-07-17Added 4 answers

No such restriction, all variables are positive/negative reals

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