Find the values of a , b so that the polyhedral...

Kendrick Hampton

Kendrick Hampton

Answered

2022-06-25

Find the values of   a , b   so that the polyhedral set defined by the system of inequalities
a x + ( b + 1 ) y 120 x + ( a + b ) y 160 ( a b ) x + y 30 x 0 y 0
has extreme direction.

Answer & Explanation

benedictazk

benedictazk

Expert

2022-06-26Added 22 answers

Solving for x , y
a x + ( b + 1 ) y = 120 x + ( a + b ) y = 160
giving
x = 40 ( 3 a b 4 ) ( a 1 ) ( a + b + 1 ) y = 40 ( 4 a 3 ) ( a 1 ) ( a + b + 1 )
Now substituting x ( a , b ) , y ( a , b ) into ( a b ) x + y = 30 we have
f ( a , b ) = 4 b 2 + 9 a 2 19 b ( 1 a ) 9 = 0
which describes the variety obeying extreme direction.

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