Algebra

Linear Programming

Medium

applied

In a linear programming problem(LPP), the maximum value of the objective function $Z = 2x + 5y$ subjected to the constraints:

$2x + 3y ≤ 6$

$2x + y ≤ 4$

$x, y ≥ 0$

is

✅ Correct Option: 2

The constraints create a bounded feasible region. The maximum value of the objective function occurs at one of the corner points of this region.

The corner points are found by examining intersections of the constraint boundaries.

At the origin:

Point: $(0, 0)$

On the $x$ -axis, set $y = 0$ :

From $2x + 3y \leq 6$ : $2x \leq 6$ , so $x \leq 3$

From $2x + y \leq 4$ : $2x \leq 4$ , so $x \leq 2$

The stricter constraint gives $x = 2$

Point: $(2, 0)$

On the $y$ -axis, set $x = 0$ :

From $2x + 3y \leq 6$ : $3y \leq 6$ , so $y \leq 2$

From $2x + y \leq 4$ : $y \leq 4$

The stricter constraint gives $y = 2$

Point: $(0, 2)$

At the intersection of $2x + 3y = 6$ and $2x + y = 4$ :

$2x + 3y = 6$

$2x + y = 4$

Subtracting the second from the first:

$2y = 2$

$y = 1$

Substituting into $2x + y = 4$ :

$2x + 1 = 4$

$2x = 3$

$x = 1.5$

Point: $(1.5, 1)$

Evaluating $Z = 2x + 5y$ at each corner point:

At $(0, 0)$ : $Z = 2(0) + 5(0) = 0$

At $(2, 0)$ : $Z = 2(2) + 5(0) = 4$

At $(0, 2)$ : $Z = 2(0) + 5(2) = 10$

At $(1.5, 1)$ : $Z = 2(1.5) + 5(1) = 3 + 5 = 8$

The maximum value of $Z$ is $10$ , occurring at the point $(0, 2)$ .

2025: 21 May Shift 1

The corner points of the bounded feasible region determined by the system of linear constraints are (0, 0), (5, 0), (3, 4) and (0, 5). Let $Z = px + qy$ where $p, q > 0$ . Condition on p and q so that the maximum of Z occurs at both (5, 0) and (3, 4) is

2026: 22 May Shift 2

Consider the LPP: Minimize $z=-50x+20y$ subject to $2x-y\ge -5, 3x+y\ge 3, 2x-3y\le 12, x\ge 0, y\ge 0$ . Then which of the following statements are TRUE?

(A) Corner points of the feasible region of the LPP are (0,5), (0,3), (1,0), (6,0).

(B) The optimum value of the objective function is -300

(D) The optimum value of the objective function is 100

Choose the correct answer from the options given below:

2022: 23 Aug Shift 1

If the objective function for an LPP is max. $(z) = 300x + 700y$ and the corner points for the bounded feasible region are $(6,0)$ $(5,0)$ $(0,6)$ $(4,4)$ and $(0,4)$ , then the maximum values of z occurs at :

2026: 22 May Shift 2

In reference to linear programming problem (LPP), which of the following statement is NOT correct?

2023: 30 May Shift 3

In a Linear Programming problem, the objective function is always :

2026: 15 May Shift 1

The corner points of a bounded feasible region are $A(15,0), B(40,0), C(4,18)$ and $D(6,12)$ . If the objective function is $z = 20x + 10y$ , then the difference in maximum and minimum value of $z$ is

In a linear programming problem(LPP), the maximum value of the objective function Z=2x+5yZ = 2x + 5yZ=2x+5y subjected to the constraints: 2x+3y≤62x + 3y ≤ 62x+3y≤6 2x+y≤42x + y ≤ 42x+y≤4 x,y≥0x, y ≥ 0x,y≥0 is

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CUET Mathematics Past Year Questions (Topic-Wise)

In a linear programming problem(LPP), the maximum value of the objective function $Z = 2x + 5y$ subjected to the constraints:

$2x + 3y ≤ 6$

$2x + y ≤ 4$

$x, y ≥ 0$

is