Linear Programming Problems — Class 12 Maths practice questions

Question 1

The maximum value of the objective function Z = 5x + 3y in a linear programming problem is attained at a:

Accepted Answer

Option (B) is correct.

Explanation: By the Corner Point Theorem, if the maximum (or minimum) value of an objective function exists for a bounded feasible region, it is always attained at one of the corner points (vertices) of the feasible region.

Question 2

The corner points of the feasible region of a Linear Programming Problem are (0, 0), (4, 0), (3, 2) and (0, 3). If the objective function is Z = 2x + 5y, then the maximum value of Z is:

Accepted Answer

Option (C) is correct.

Explanation: By the Corner-Point Method, the maximum value of Z occurs at one of the corner points of the feasible region. Evaluating Z = 2x + 5y at each corner point:

At (0, 0): Z = 2(0) + 5(0) = 0
At (4, 0): Z = 2(4) + 5(0) = 8
At (3, 2): Z = 2(3) + 5(2) = 6 + 10 = 16
At (0, 3): Z = 2(0) + 5(3) = 15

∴ Maximum value of Z = 16 at (3, 2).

Question 3

The corner points of the feasible region of a Linear Programming Problem are (0, 0), (4, 0), (3, 2) and (0, 3). If the objective function is Z = 5x + 2y, then the maximum value of Z is:

Accepted Answer

Option (C) is correct.

Explanation: By the Corner-Point Method, the maximum value of a linear objective function over a bounded feasible region occurs at one of the corner points. Evaluating Z = 5x + 2y at each corner point:

At (0, 0): Z = 5(0) + 2(0) = 0
At (4, 0): Z = 5(4) + 2(0) = 20
At (3, 2): Z = 5(3) + 2(2) = 15 + 4 = 19
At (0, 3): Z = 5(0) + 2(3) = 6

∴ Maximum value of Z = 20 at corner point (4, 0).

Question 4

The corner points of the feasible region of a Linear Programming Problem are (0, 0), (4, 0), (3, 2) and (0, 3). If the objective function is Z = 5x + 2y, then the maximum value of Z is:

Accepted Answer

Option (B) is correct.

Explanation: By the Corner-Point Method, the maximum value of Z occurs at one of the corner points of the feasible region. Evaluating Z = 5x + 2y at each corner point:

At (0, 0): Z = 5(0) + 2(0) = 0
At (4, 0): Z = 5(4) + 2(0) = 20
At (3, 2): Z = 5(3) + 2(2) = 15 + 4 = 19
At (0, 3): Z = 5(0) + 2(3) = 6

∴ Maximum value of Z = 20 at corner point (4, 0).

Question 5

The corner points of the feasible region of a Linear Programming Problem are O(0, 0), A(4, 0), B(2, 3) and C(0, 5). If the objective function is Z = 3x + 2y, then the maximum value of Z is:

Accepted Answer

Option (B) is correct.

Explanation: By the Corner-Point Method, the maximum value of Z = 3x + 2y is found by evaluating Z at each corner point of the feasible region.

At O(0, 0): Z = 3(0) + 2(0) = 0
At A(4, 0): Z = 3(4) + 2(0) = 12
At B(2, 3): Z = 3(2) + 2(3) = 6 + 6 = 12
At C(0, 5): Z = 3(0) + 2(5) = 10

∴ Maximum value of Z = 12.

Question 6

The feasible region of a Linear Programming Problem (LPP) is always:

Accepted Answer

Option (B) is correct.

Explanation: By definition, the feasible region of a Linear Programming Problem is the set of all points satisfying all the given constraints simultaneously. Since each constraint is a linear inequality whose solution set is a half-plane (a convex set), and the intersection of any number of convex sets is also a convex set, the feasible region of an LPP is always a convex set.

Linear Programming Problems: Class 12 Maths Practice Questions

Want unlimited practice on Linear Programming Problems?