Questions on Linear Programming Problem (LPP) Graphical Method

Question 1: Maximize $z = 15x_1 +10 x_2$

Subject to,

$4x_1\ + 6x_2 \le 360$

$3x_1\ +\ 0x_2 \le 180$

$0x_1\ + 5x_2\le 200$

$x_1,x_2\ge 0$

Ans: (60,20) and 1100

Question 2: Maximize $z=2x_1\ + x_2$

Subject to,

$x_1\ + 2x_2 \le 10$

$x_1\ -x_2 \le 2$

$x_1\ +x_2\le 6$

$x_1-2x_2 \le1$

$x_1,x_2\ge 0$

Ans: (4,2) and 10

Question 3: Minimize $z=3x_1+2x_2$

Subject to,

$5x_1\ + x_2 \ge 10$

$x_1+x_2\ge 6$

$x_1\ +4x_2 \ge 12$

$x_1,x_2\ge 0$

Ans: (1,5) and 13

Question 4: Minimize $z=20x_1\ + 10x_2$

Subject to,

$x_1 \ + 2x_2 \le 40$

$3x_1\ +x_2 \ge30$

$4x_1+3x_2 \ge 60$

$x_1,x_2\ge 0$

Ans: (6,12) and 240

Question 5: Minimize $z=6x_1+24x_2$

Subject to,

$x_1+2x_2 \ge 3$

$x+4x_2\ge 4$

$x_1,x_2\ge 0$

Ans: (4,0) and (3,0.25) and 24

Question 6: Maximize $z=45x_1 + 80x_2$

Subject to,

$5x_1+20x_2 \le 400$

$10x_1+15x_2 \le 450$

$x_1,x_2\ge 0$

Question 7: Minimize $z=3x_1 +2x_2$

Subject to,

$x_1-x_2\le 1$

$x_1+x_2 \ge 3$

$x_1,x_2\ge 0$

Question 8: Minimize $z=7x_1+8x_2$

Subject to,

$3x_1+x_2\ge 8$

$x_1 + 3x_2\ge 11$

$x_1,x_2\ge 0$

Question 9: Maximize $z=120x_1+100x_2$

Subject to,

$10x_1+5x_2\le 80$

$6x_1+6x_2\le 66$

$4x_1+8x_2\ge 24$

$x_1,x_2\ge 0$

Question 10: Maximize $z=5x_1+7x_2$

Subject to,

$x_1+x_2 \le 4$

$3x_1+8x_2\le 24$

$10x_1+7x_2\le 35$

$x_1,x_2\ge 0$

Question 11: Mazimize $z=40x_1+30x_2$

Subject to,

$x_1\le 16$

$x_2\le 8$

$x_1+2x_2\le 24$

$x_1,x_2\ge 0$

Question 12: Maximize $z=6x_1+4x_2$

Subject to,

$-2x_1+x_2\le 2$

$x_1-x_2\le 2$

$3x_1+2x_2\le9$

$x_1,x_2\ge 0$

Ans:($x_1$=13/5 or 5/7,$x_2$=3/5 or2/7) and 18

Question 13: Maximize $z=3x_1+4x_2$

Subject to,

$5x_1+4x_2\le 200$

$3x_1+5x_2\le150$

$5x_1+4x_2\ge 100$

$8x_1+4x_2\ge 80$

$x_1,x_2\ge 0$

Ans: (30.8,11.5) and 138.4

Question 14: Maximize $z=5x_1+7x_2$

Subject to,

$x_1+x_2\le 4$

$3x_1+8x_2\le24$

$10x_1+7x_2\le 35$

$x_1,x_2\ge 0$

Ans: (1.6,2.4) and (24.8)

Question 15: Maximize $z=5x_1+3x_2$

Subject to,

$3x_1+5x_2\le 15$

$5x_1+2x_2\le10$

$x_1,x_2\ge 0$

Ans: (20/19,45/19) and 235/19

Question 16: Maximize $z=8x_1+7x_2$

Subject to,

$3x_1+x_2\le 66$

$x_1+x_2\le 45$

$x_1\le 20$

$x_2\le 40$

$x_1,x_2\ge 0$

Ans: (21/2,69/2) and 325.5

Question 17: Minimize $z= 20x_1+10x_2$

Subject to,

$x_1+2x_2\le 40$

$3x_1+x_2\ge 30$

$4x_1+3x_2\ge 60$

$x_1,x_2\ge 0$

Ans: (6,12) and 140

Question 18: Minimize $z=x_1-7x_2+190$

Subject to,

$x_1+x_2\le 8$

$x_1\le5$

$x_2\le 5$

$x_1+x_2\ge4$

$x_1,x_2\ge 0$

Ans: (0,5) and 155

Question 19: Minimize $z=x_1-5x_2+20$

Subject to,

$x_1-x_2\ge 0$

$-x_1+2x_2\ge 2$

$x_1\ge 3$

$x_2\ge 4$

$x_1,x_2\ge 0$

Ans: (4,4) and 4