Solve the following LPP graphically :

Minimise z = 5x + 7y subject to the constraints

2x + y \geq 8

x + 2y \geq 10

x, y \geq 0

 

 
 
 
 
 

Answers (1)
S safeer

Given: Constrains

2x + y \geq 8

x + 2y \geq 10

x, y \geq 0

Corner points A(0,8), B(2,4), C(10,0)

z = 5x + 7y

At point A(0,8) 

z = 5 \times 0 + 7 \times 8 = 56

At point B(2,4) 

z = 5 \times 2 + 7 \times 4 = 38 \ $ (Min)

At point A(10,0) 

z = 5 \times 10 + 7 \times 0 = 50

Now to check whether the smallest value of z = 38 is the minimum value or not draw a plane 5x + 7y < 38.

This plane doesn't have any common point with the possible feasible region except (2, 4).

Hence the minimum value of z = 38 at x = 2 and y = 4.

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