Answer to Question #173571 in Operations Research for ANJU JAYACHANDRAN

Question

5. (a) Use the simplex method to solve the following L.P.P. (5)

Max 4 1 3 2

z = x + x

Subject to

2x1 + x2 ≤1000

x1 + x2 ≤ 800

400 x1 ≤

x2 ≤ 700

.0 , x1

x2 ≥

Answer 1

simplex method is too long to explain here you cn studied at https://www.britannica.com/topic/simplex-method

$2x_1 + x_2 ≤1000\\ x_1 + x_2 ≤ 800\\x_1,x_2\ge0$

$Z=4x_1+3x_2$

The graphical region of the given inequalities is-

The critical points are-

(200,600)  $Z=4x_1+3x_2=4(200)+3(600)=800+1800=2600$

(500,0) $Z=4x_1+3x_2=4(500)+3(0)=2000+0=2000$

(0,800) $Z=4x_1+3x_2=4(200)+3(600)=0+2400=2400$

(0,0) $Z=4x_1+3x_2=4(0)+3(0)=0+0=0$

The maximum value of Z is 2600 at $x_1=200,x_2=600$