Question

solve the following L.P.P graphically, minimize z=4x+5y subject to 5x+y\10
2x+2y\12
x+4y\12
x\0,y\0
​

Answer 1

Given : 5x + y    ≥ 10  , 2x + 2y  ≥ 12   C = x  + 4y   ≥ 12

x ≥ 0  , y ≥ 0

To Find : minimize z=4x+5y

Solution:

5x + y    ≥ 10

2x + 2y  ≥ 12  => x + y ≥  6

x  + 4y   ≥ 12

x≥ 0  y ≥ 0  

Cost Z = 4x+5y

Boundary points are

( 0 , 10) , (1 , 5) , ( 4 , 2) and (12 , 0)

Z =4x + 5y

x =  0  , y = 10   z  = 50

x =  1  , y = 5      z  = 29

x =  4  , y = 2     z  = 26

x =  12  , y =  0   z  = 48

Hence minimum cost  26 when x = 4 and y = 2

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