Algebra

Linear Programming

Medium

core

The feasible region of a LPP is bounded. The corresponding objective function is Z= 6x - 7y. Then objective function attains:

Only maximum in the feasible region

Only minimum in the feasible region

both maximum and minimum in the feasible region

either maximum or minimum but not both in the feasible region.

✅ Correct Option: 3

The feasible region of the LPP is bounded, which means it forms a closed and limited shape with clear boundaries.

The objective function is given as $Z = 6x - 7y$ .

For any bounded feasible region in Linear Programming, the objective function is continuous over a closed and bounded set.

By the Extreme Value Theorem, a continuous function over a closed and bounded region must attain both its maximum and minimum values within that region.

In Linear Programming, these extreme values occur at the corner points (vertices) of the feasible region.

Since the region is bounded:

The objective function $Z = 6x - 7y$ cannot approach infinity or negative infinity.

The function must have a largest value (maximum) at some corner point.

The function must have a smallest value (minimum) at some corner point.

Both the maximum and minimum values are guaranteed to exist because the feasible region is bounded.

If the region were unbounded, the objective function might approach infinity in some direction, and only one extreme value (or neither) might exist.

Therefore, the objective function attains both maximum and minimum in the feasible region.

2025: 22 May Shift 2

The maximum value of the objective function $z = 10x + 15y$ of an L.P.P. subjected to the constraints

$2x + 4y \leq 8$ ,

$3x + y \leq 6$ ,

$-x - y \geq -4$ ,

$x \geq 0$ , $y \geq 0$ is:

2026: 31 May Shift 2

The feasible region for a LPP is shown in the given figure. The maximum value of $z = 2x + 5y$ is :

2025: 26 May Shift 2

If the objective function z = 4x + 3y has maximum value on a line joining points (3, a) and (b, 2) where a > 0, b > 0 such that a - b = 2, then the maximum value of z is:

2023: 30 May Shift 3

The corner points 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.

Column - A	Column - B
Maximum value of z	350

2025: 14 May Shift 1

The corner points of the feasible region associated with the LPP: Maximise $Z = px + qy$ , $p,q > 0$ subject to $2x + y \leq 10$ , $x + 3y \leq 15$ , $x, y \geq 0$ are (0, 0), (5, 0), (3, 4) and (0, 5). If optimum value occurs at both (3, 4) and (0, 5), then

2022: 25 May Shift 1

The programming problem

Max $Z = 2x + 3y$ subject to the conditions $0 \leq x \leq 3, 0 \leq y \leq 4$ is :

The feasible region of a LPP is bounded. The corresponding objective function is Z= 6x - 7y. Then objective function attains:

Solution

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