Linear Programming Class 12 MCQs Questions with Answers

1. Maximize Z = 10 x1 + 25 x2, subject to 0 ≤ x1 ≤ 3, 0 ≤ x2 ≤ 3, x1 + x2 ≤ 5

2. The feasible region for an LPP is shown shaded in the following figure. Minimum of Z = 4x + 3y occurs at the point

3. Z = 20×1 + 20×2, subject to x1 ≥ 0, x2 ≥ 0, x1 + 2×2 ≥ 8, 3×1 + 2×2 ≥ 15, 5×1 + 2×2 ≥ 20. The minimum value of Z occurs at

4. Minimize Z = 20×1 + 9×2, subject to x1 ≥ 0, x2 ≥ 0, 2×1 + 2×2 ≥ 36, 6×1 + x2 ≥ 60.

5. Let R be the feasible region for a linear programming problem and let Z = ax + by be the objective function. If R is bounded, then the objective function Z has both a maximum and a minimum value on R and

6. Z = 7x + y, subject to 5x + y ≥ 5, x + y ≥ 3, x ≥ 0, y ≥ 0. The minimum value of Z occurs at

7. In equation 3x – y ≥ 3 and 4x – 4y > 4

8. Find the maximum value of z = 3x + 4y subject to constraints x + y ≤ 4 , x ≥ 0 and y ≥ 0​

9. In solving the LPP:

“minimize f = 6x + 10y subject to constraints x ≥ 6, y ≥ 2, 2x + y ≥ 10, x ≥ 0, y ≥ 0” redundant constraints are

10. Of all the points of the feasible region for maximum or minimum of objective function the points

11. The maximum value of the object function Z = 5x + 10 y subject to the constraints x + 2y ≤ 120, x + y ≥ 60, x – 2y ≥ 0, x ≥ 0, y ≥ 0 is

12. Maximise the function Z = 11x + 7y, subject to the constraints: x ≤ 3, y ≤ 2,x ≥ 0, y ≥ 0.

13. A toy company manufactures two types of toys A and B. Demand for toy B is atmost half of that if type A. Write the corresponding constraint if x toys of type A and y toys of type B are manufactured.

14. In linear programming feasible region (or solution region) for the problem is

15. Shape of the feasible region formed by the following constraints is x + y ≤ 2, x + y ≥ 5, x ≥ 0, y ≥ 0​

16. The region represented by the inequalities

x ≥ 6, y ≥ 2, 2x + y ≤ 0, x ≥ 0, y ≥ 0 is

17. Maximize Z = 3x + 5y, subject to x + 4y ≤ 24, 3x + y ≤ 21, x + y ≤ 9, x ≥ 0, y ≥ 0

18. The feasible region for a LPP is shown shaded in the figure. Let Z = 3x – 4y be the objective function. Minimum of Z occurs at

19. Minimise Z = 13x – 15y subject to the constraints : x + y ≤ 7, 2x – 3y + 6 ≥ 0 , x ≥ 0, y ≥ 0.

20. The corner point of the feasible region determined by the system of linear constraints are (0, 0), (0, 40), (20, 40), (60, 20), (60, 0). The objective function is Z = 4x + 3y.

Compare the quantity in Column A and Column B