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Class 12 Maths Chapter 12: Linear Programming Assertion-reason questions with answers

2 assertion-reason questions on Linear Programming, each with its answer and the reason, written from the NCERT chapter. For the CBSE board and JEE Main, which are set from the same NCERT chapter. Open a question's solution to check your working; then take the free test to find your next chapter. Each question gives an Assertion (A) and a Reason (R); choose how they stand to each other.

Question 1
Assertion (A): For a linear programming problem whose feasible region is unbounded, the objective function may have no maximum value. Reason (R): A feasible region is bounded if it can be enclosed within a circle.
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Answer: (b) Both A and R are true, but R is not the correct explanation of A.

A is true: if R is unbounded, a maximum or minimum of the objective function may not exist. R is true: it is the definition of a bounded region. But R only defines boundedness; it does not explain why an optimum can fail to exist on an unbounded region, so R is not the correct explanation of A.

Question 2
Assertion (A): If Z = 3x + 6y takes its minimum value on a feasible region at both corner points (2, 2) and (4, 1), then Z takes the same minimum value at (3, 1.5). Reason (R): If two corner points produce the same minimum value of the objective function, every point on the line segment joining them gives the same minimum value.
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Answer: (a) Both A and R are true, and R is the correct explanation of A.

Z(2, 2) = 18 and Z(4, 1) = 18. (3, 1.5) is the midpoint of the segment joining them, and Z(3, 1.5) = 9 + 9 = 18. R is the general feature that makes A true, so R correctly explains A.

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