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Mathematics : Linear Programming

Long Answer Type

11. Minimize z = 2x + 3y, such that 1 ≤ x + 2y ≤ 10, x ≥ 0, y ≥ 0.

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12. Solve the following linear programming problem graphically:
Minimise Z = 200x + 500y
subject to the constraints x + 2y ≥ 10, 3x + 4 y ≤ 24, x ≥ 0, y ≥ 0

111 Views

13.

Solve the following problem graphically:
Minimise and Maximise Z = 3x + 9y
subject to the constraints:
x + 3y ≤ 60
x + y ≥ 10
x ≤ y
x ≥ 0, y ≥ 0

413 Views

14. Show that the minimum of Z occurs at more than two points.
Minimise and Maximise Z = 5x + 10y subject to constraints x + 2y ≤ 120, x + y ≥ 60, x - 2 y ≥ 0, x, y ≥ 0.

107 Views

15. Minimize z = 5x + 7y such that 2x + y ≥ 8, x + 2y ≥ 10, x, y ≥ 0.

94 Views

16. Show that the minimum of Z occurs at more than two points.
Minimise and Maximise Z = x + 2y subject to constraints x + 2y ≥ 100, 2x - y ≤ 0, 2x + y ≤ 200, x, y ≥ 0

115 Views

17. Determine graphically the minimum value of the objective function
Z = - 50x + 20y subject to the constraints 2x - y ≥ - 5, 3x + y ≥ 3, 2x - 3 y ≤ 12, x ≥ 0, y ≥ 0

151 Views

18.

Solve the following linear programming problem graphically:
Minimise Z = 3x + 5y subject to the constraints:x + 3y ≥ 3, x + y ≥ 2, x, y ≥ 0

115 Views

19. Solve the following linear programming problem graphically:
Minimise Z = x + 2y subject to the constraints 2x + y ≥ 3, x + 2y ≥ 6, x, y ≥ 0

91 Views

20. Solve the following linear programming problem graphically:
Maximise Z = - x + 2y, subject to the constraints: x ≥ 3, x + y ≥ 5, x + 2 y ≥ 6, y ≥ 0.

80 Views