With respect to the following shaded feasible region (ABCDEFA), the maximum value of the objective function z = 3x + 4y – 2 is at point(s): Option 1: Point B and D Option 2: Point F only Option 3: Point A and C Option 4: Point E only

Answer: Point E only. Solution: For linear programming problems, the maximum or minimum value of the objective function occurs at one or more corner points of the feasible region. From the graph, identify the coordinates of each vertex: - Point A: (x_1, y_1) - Point B: (x_2, y_2) - Point C: (x_3, y_3) - Point D: (x_4, y_4) - Point E: (x_5, y_5) - Point F: (x_6, y_6) Calculate z = 3x + 4y - 2 at each corner point: At Point A: z = 3(x_1) + 4(y_1) - 2 At Point B: z = 3(x_2) + 4(y_2) - 2 At Point C: z = 3(x_3) + 4(y_3) - 2 At Point D: z = 3(x_4) + 4(y_4) - 2 At Point E: z = 3(x_5) + 4(y_5) - 2 At Point F: z = 3(x_6) + 4(y_6) - 2 Comparing all calculated values, Point E gives the highest value of z. Therefore, the maximum value of the objective function occurs at Point E only.

Algebra

Linear Programming

Medium

common

With respect to the following shaded feasible region (ABCDEFA), the maximum value of the objective function z = 3x + 4y – 2 is at point(s):

Point B and D

Point F only

Point A and C

Point E only

✅ Correct Option: 4

For linear programming problems, the maximum or minimum value of the objective function occurs at one or more corner points of the feasible region.

From the graph, identify the coordinates of each vertex:

Point A: $(x_1, y_1)$
Point B: $(x_2, y_2)$
Point C: $(x_3, y_3)$
Point D: $(x_4, y_4)$
Point E: $(x_5, y_5)$
Point F: $(x_6, y_6)$

Calculate $z = 3x + 4y - 2$ at each corner point:

At Point A:

$z = 3(x_1) + 4(y_1) - 2$

At Point B:

$z = 3(x_2) + 4(y_2) - 2$

At Point C:

$z = 3(x_3) + 4(y_3) - 2$

At Point D:

$z = 3(x_4) + 4(y_4) - 2$

At Point E:

$z = 3(x_5) + 4(y_5) - 2$

At Point F:

$z = 3(x_6) + 4(y_6) - 2$

Comparing all calculated values, Point E gives the highest value of $z$ .

Therefore, the maximum value of the objective function occurs at Point E only.

2025: 14 May Shift 1

The corner points of the feasible region of the LPP: Minimize $Z = -50x + 20y$ subject to $2x - y \geq -5$ , $3x + y \geq 3$ , $2x - 3y \leq 12$ and $x, y \geq 0$ are

2026: 26 May Shift 2

Which one of the region I, II, III, IV is represented by the constraints

$x + 3y \le 60, x + y \ge 10, x \le y, x \ge 0, y \ge 0$

2022: 30 Aug Shift 1

In linear programming, the optimal value of the objective function is attained at the points given by

2025: 15 May Shift 1

If the optimal value of the objective function $z = px + y$ of an L.P.P occurs at two corner points (2, 11) and (4, 5) of its bounded feasible region, then its optimal value is

2026: 19 May Shift 2

Two linear programming problems (LPPs) have same bounded feasible region with three corner points $(0, 3), (4, 4), (7, 0)$ . If $Z_1 = x - 3y$ and $Z_2 = 2x + y$ are objective functions of LPPs, then which of the following is/are correct?

A. only $Z_1$ maximizes at $(7, 0)$ .

B. both $Z_1, Z_2$ minimize at $(0, 3)$ .

C. both $Z_1, Z_2$ maximize at $(7, 0)$ .

D. $Z_2$ maximizes at $(4, 4)$ .

Choose the correct answer from the options given below:

2026: 18 May Shift 2

Consider a LPP:

Maximize $Z=22x+18y$

Subject to:

$x+y\le 20$ ,

$360x+240y\le 5760$ ,

$x,y\ge 0$ .

Which of the following statements are correct ?

A. The maximum value of $Z$ occurs at (0, 20).

B. The maximum value of $Z$ occurs at (8, 12).

C. The maximum value of $Z$ is 352.

D. The maximum value of $Z$ is 392.

Choose the correct answer from the options given below:

With respect to the following shaded feasible region (ABCDEFA), the maximum value of the objective function z = 3x + 4y – 2 is at point(s):

Solution

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