Algebra

Linear Programming

Medium

core

The maximum value of the objective function $z = 2x + 3y$ of an L.P.P. subjected to the constraints $x - y \le 1$ , $x + y \le 3$ , $x, y \ge 0$ is

✅ Correct Option: 2

The objective function is $z = 2x + 3y$ with constraints:

$x - y \le 1$

$x + y \le 3$

$x \ge 0$

$y \ge 0$

The feasible region is bounded by the constraint lines. The corner points are found at the intersections of these boundary lines.

At the origin:

Point: $(0, 0)$

Where $x = 0$ meets $x + y = 3$ :

$0 + y = 3$

$y = 3$

Point: $(0, 3)$

Where $y = 0$ meets $x - y = 1$ :

$x - 0 = 1$

$x = 1$

Point: $(1, 0)$

Where $x - y = 1$ meets $x + y = 3$ :

From $x - y = 1$ : $x = y + 1$

Substituting into $x + y = 3$ :

$(y + 1) + y = 3$

$2y + 1 = 3$

$2y = 2$

$y = 1$

$x = 2$

Point: $(2, 1)$

The corner points of the feasible region are: $(0, 0)$ , $(0, 3)$ , $(1, 0)$ , and $(2, 1)$ .

Evaluating the objective function at each corner point:

At $(0, 0)$ : $z = 2(0) + 3(0) = 0$

At $(0, 3)$ : $z = 2(0) + 3(3) = 9$

At $(1, 0)$ : $z = 2(1) + 3(0) = 2$

At $(2, 1)$ : $z = 2(2) + 3(1) = 4 + 3 = 7$

The maximum value of $z$ is $9$ , occurring at the point $(0, 3)$ .

2026: 14 May Shift 2

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2025: 15 May Shift 2

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The corner points of the bounded feasible region for an LPP are (0, 20), (3,12), (6,8), and (0,15). The objective function is $Z = \alpha x + \beta y$ , where $\alpha, \beta > 0$ . If the maximum of Z occurs at the corner points (3,12) and (6,8), then the relationship between $\alpha$ and $\beta$ is:

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Consider the linear programming problem :

Minimize $z = 50x + 70y$

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The minimum value of objective function is :

2025: 16 May Shift 1

Consider the following L.L.P.

Minimize z = 30x - 30y + 1800;

subject to x + y ≤ 30, x ≤ 15, y ≤ 20, x + y ≥ 15 and x, y ≥ 0.

Then it attains its optimal value at the point

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 :

The maximum value of the objective function z=2x+3yz = 2x + 3yz=2x+3y of an L.P.P. subjected to the constraints x−y≤1x - y \le 1x−y≤1, x+y≤3x + y \le 3x+y≤3, x,y≥0x, y \ge 0x,y≥0 is

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The maximum value of the objective function $z = 2x + 3y$ of an L.P.P. subjected to the constraints $x - y \le 1$ , $x + y \le 3$ , $x, y \ge 0$ is