Algebra

Linear Programming

Medium

core

The sum of the x-coordinates of the corner points of the feasible region for the LPP: Minimize $z = 3x + 2y$ subject to constraints $x + y \leq 14$ , $x \geq 4$ , $x \leq 8, y \geq 0$ is

✅ Correct Option: 4

We need to find the corner points of the feasible region and add up their $x$ -coordinates.

The constraints are:

$x + y \leq 14$

$x \geq 4$

$x \leq 8$

$y \geq 0$

The corner points occur where these boundary lines intersect.

Where $x = 4$ meets $y = 0$ :

Point: $(4, 0)$

$x$ -coordinate $= 4$

Where $x = 4$ meets $x + y = 14$ :

Substituting $x = 4$ :

$4 + y = 14$

$y = 10$

Point: $(4, 10)$

$x$ -coordinate $= 4$

Where $x = 8$ meets $x + y = 14$ :

Substituting $x = 8$ :

$8 + y = 14$

$y = 6$

Point: $(8, 6)$

$x$ -coordinate $= 8$

Where $x = 8$ meets $y = 0$ :

Point: $(8, 0)$

$x$ -coordinate $= 8$

Sum of $x$ -coordinates:

$4 + 4 + 8 + 8 = 24$

Answer: $24$

2022: 4 Aug Shift 1

A feasible solution is :

2025: 13 May Shift 2

The feasible region of the linear programming problem is represented below:

The constraints of this LPP are

2026: 26 May Shift 2

If the feasible region (shaded portion)of a LPP is as shown in the graph, then max $z = 50x + 15y$ is:

2025: 14 May Shift 2

Consider the linear programming problem(LPP):

Minimize $Z = x + y$

$x + 2y \leq 4,$

$3x + y \geq 3,$

$4x + 3y \geq 6,$

$x, y \geq 0.$

Which of the following is correct for the above linear programming problem (LPP):

(A) The LPP has a bounded feasible region.

(B) The LPP has a unique optimal solution.

(D) The corner points of the feasible region are (3/2, 0), (3/5, 6/5), (2/5, 6/5) and (4, 0)

Choose the correct answer from the options given below:

2025: 21 May Shift 2

The corner points of the bounded feasible region determined by the system of linear constraints are $(0, 0)$ , $(5, 0)$ , $(6, 5)$ , $(6, 8)$ , $(4, 10)$ , $(0, 8)$ . Let $Z = 3x - 4y$ be the objective function. The minimum value of Z occurs at

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

The sum of the x-coordinates of the corner points of the feasible region for the LPP: Minimize z=3x+2yz = 3x + 2yz=3x+2y subject to constraints x+y≤14x + y \leq 14x+y≤14, x≥4x \geq 4x≥4, x≤8,y≥0x \leq 8, y \geq 0x≤8,y≥0 is

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The sum of the x-coordinates of the corner points of the feasible region for the LPP: Minimize $z = 3x + 2y$ subject to constraints $x + y \leq 14$ , $x \geq 4$ , $x \leq 8, y \geq 0$ is