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