If the extreme points of a bounded convex region of R2 are (1, 1), (3, 4), (4,4) and (5,5) then what is the maximum value of 3y – 2x on this region?

foyerir

foyerir

Answered question

2022-09-06

If the extreme points of a bounded covex region of R 2 are ( 1 , 1 ) , ( 3 , 4 ) , ( 4 , 4 ) and ( 5 , 5 ) then what is the maximum value of 3y -2x.

Answer & Explanation

Andrejkoxg

Andrejkoxg

Beginner2022-09-07Added 20 answers

Let 3y-2x=P
Now to find the maximum value of function P on the given extreme points.
(1,1),(3,4),(4,4) and (5,5)
P ( x , y ) = 3 y 2 x P ( 1 , 1 ) = 3 × 1 2 × 1 = 1 P ( 3 , 4 ) = 3 × 4 2 × 3 = 12 6 = 6 P ( 4 , 4 ) = 3 × 4 2 × 4 = 12 8 = 4 P ( 5 , 5 ) = 3 × 5 2 × 5 = 15 10 = 5
Hence we see that function P=3y-2x has maximum value at extreme point (3,4) and the minimum value of the function is 6.

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