Linear Programming Class 12 MCQs Questions with Answers

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

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

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

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

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

6. 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

7. 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.

8. 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

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

10. 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

11. The region represented by the inequalities

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

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

13. 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

14. 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

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

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

17. 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 

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

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

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