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Linear Programming

Every solved example, exercise, and miscellaneous question — in the order the textbook teaches them. · 15 questions

12.2.2 Graphical Method of Solving Linear Programming Problems

15 q

Solved Examples

Worked · 5
  1. 12.1 Eg.1
    Solve the following linear programming problem graphically: Maximise Z=4x+yZ = 4x + y subject to the constraints: x+y≤50x + y \le 50 3x+y≤903x + y \le 90 x≥0x \ge 0, y≥0y \ge 0
  2. 12.1 Eg.2
    Solve the following linear programming problem graphically: Minimise Z=200x+500yZ = 200x + 500y subject to the constraints: x+2y≥10x + 2y \ge 10 3x+4y≤243x + 4y \le 24 x≥0x \ge 0, y≥0y \ge 0
  3. 12.1 Eg.3
    Solve the following problem graphically: Minimise and Maximise Z=3x+9yZ = 3x + 9y subject to the constraints: x+3y≤60x + 3y \le 60 x+y≥10x + y \ge 10 x≤yx \le y x≥0x \ge 0, y≥0y \ge 0
  4. 12.1 Eg.4
    Determine graphically the minimum value of the objective function Z=−50x+20yZ = -50x + 20y subject to the constraints: 2x−y≥−52x - y \ge -5 3x+y≥33x + y \ge 3 2x−3y≤122x - 3y \le 12 x≥0x \ge 0, y≥0y \ge 0
  5. 12.1 Eg.5
    Minimise Z=3x+2yZ = 3x + 2y subject to the constraints: x+y≥8x + y \ge 8 3x+5y≤153x + 5y \le 15 x≥0x \ge 0, y≥0y \ge 0

Exercise 12.1

Practice · 10
  1. Ex 12.1 Q1
    Solve the following Linear Programming Problem graphically: Maximise Z=3x+4yZ = 3x + 4y subject to the constraints : x+y≤4x + y \le 4, x≥0x \ge 0, y≥0y \ge 0.
  2. Ex 12.1 Q2
    Solve the following Linear Programming Problem graphically: Minimise Z=−3x+4yZ = -3x + 4y subject to x+2y≤8x + 2y \le 8, 3x+2y≤123x + 2y \le 12, x≥0x \ge 0, y≥0y \ge 0.
  3. Ex 12.1 Q3
    Solve the following Linear Programming Problem graphically: Maximise Z=5x+3yZ = 5x + 3y subject to 3x+5y≤153x + 5y \le 15, 5x+2y≤105x + 2y \le 10, x≥0x \ge 0, y≥0y \ge 0.
  4. Ex 12.1 Q4
    Solve the following Linear Programming Problem graphically: Minimise Z=3x+5yZ = 3x + 5y such that x+3y≥3x + 3y \ge 3, x+y≥2x + y \ge 2, x,y≥0x, y \ge 0.
  5. Ex 12.1 Q5
    Solve the following Linear Programming Problem graphically: Maximise Z=3x+2yZ = 3x + 2y subject to x+2y≤10x + 2y \le 10, 3x+y≤153x + y \le 15, x,y≥0x, y \ge 0.
  6. Ex 12.1 Q6
    Solve the following Linear Programming Problem graphically: Minimise Z=x+2yZ = x + 2y subject to 2x+y≥32x + y \ge 3, x+2y≥6x + 2y \ge 6, x,y≥0x, y \ge 0. Show that the minimum of ZZ occurs at more than two points.
  7. Ex 12.1 Q7
    Solve the following Linear Programming Problem graphically: Minimise and Maximise Z=5x+10yZ = 5x + 10y subject to x+2y≤120x + 2y \le 120, x+y≥60x + y \ge 60, x−2y≥0x - 2y \ge 0, x,y≥0x, y \ge 0.
  8. Ex 12.1 Q8
    Solve the following Linear Programming Problem graphically: Minimise and Maximise Z=x+2yZ = x + 2y subject to x+2y≥100x + 2y \ge 100, 2x−y≤02x - y \le 0, 2x+y≤2002x + y \le 200; x,y≥0x, y \ge 0.
  9. Ex 12.1 Q9
    Solve the following Linear Programming Problem graphically: Maximise Z=−x+2yZ = -x + 2y, subject to the constraints: x≥3x \ge 3, x+y≥5x + y \ge 5, x+2y≥6x + 2y \ge 6, y≥0y \ge 0.
  10. Ex 12.1 Q10
    Solve the following Linear Programming Problem graphically: Maximise Z=x+yZ = x + y, subject to x−y≤−1x - y \le -1, −x+y≤0-x + y \le 0, x,y≥0x, y \ge 0.