Algebra

Linear Programming

Medium

core

The corner points of the bounded feasible region of the LPP: Maximize $z = x + y$ subject to constraints $2x + 5y \leq 100$ , $8x + 5y \leq 200$ , $x \geq 0$ , $y \geq 0$ are

$(0,0), (25,0), (0,20), \left(\frac{50}{3}, \frac{40}{3}\right)$

$(25,0), (20,0), \left(\frac{50}{3}, \frac{40}{3}\right), (50,0)$

$(0,20), (0,40), (50,0), (25,0)$

$(0,0), (50,0), (0,20), \left(\frac{50}{3}, \frac{40}{3}\right)$

✅ Correct Option: 1

The corner points of the feasible region occur where the boundary lines intersect.

The boundary lines from the constraints are:

$2x + 5y = 100$
$8x + 5y = 200$
$x = 0$ (y-axis)
$y = 0$ (x-axis)

Intersection of $x = 0$ and $y = 0$ :

Point: $(0, 0)$

Intersection of $x = 0$ and $2x + 5y = 100$ :

$5y = 100$

$y = 20$

Point: $(0, 20)$

Intersection of $x = 0$ and $8x + 5y = 200$ :

$5y = 200$

$y = 40$

Point: $(0, 40)$

Checking $2x + 5y \leq 100$ :

$2(0) + 5(40) = 200 \not\leq 100$

This point is outside the feasible region.

Intersection of $y = 0$ and $2x + 5y = 100$ :

$2x = 100$

$x = 50$

Point: $(50, 0)$

Checking $8x + 5y \leq 200$ :

$8(50) + 5(0) = 400 \not\leq 200$

This point is outside the feasible region.

Intersection of $y = 0$ and $8x + 5y = 200$ :

$8x = 200$

$x = 25$

Point: $(25, 0)$

Intersection of $2x + 5y = 100$ and $8x + 5y = 200$ :

$8x + 5y = 200$

$-(2x + 5y = 100)$

$6x = 100$

$x = \frac{50}{3}$

Substituting into $2x + 5y = 100$ :

$2\left(\frac{50}{3}\right) + 5y = 100$

$\frac{100}{3} + 5y = 100$

$5y = 100 - \frac{100}{3}$

$5y = \frac{200}{3}$

$y = \frac{40}{3}$

Point: $\left(\frac{50}{3}, \frac{40}{3}\right)$

The corner points of the bounded feasible region are:

$(0,0)$ , $(25,0)$ , $(0,20)$ , $\left(\frac{50}{3}, \frac{40}{3}\right)$

2025: 27 May Shift 1

For the LPP: minimize $z = 6x + 3y$ subject to the constraints

$4x + y \geq 80$

$x + 5y \geq 115$

$3x + 2y \leq 150$

$x \geq 0, y \geq 0$ then the minimum value of z is

2025: 30 May Shift 2

In an LPP, the feasible region represented by the set off constraints $2x + 3y \leq 18$ , $x + y \leq 10$ , $x \geq 0$ , $y \geq 0$ is

2026: 22 May Shift 1

A manufacturer produces two products, A and B. Both products are processed on two different machines. The available capacity of the first machine is 12 hours and of second machine is 9 hours per day. Each unit of product A requires 3 hours on both machines and each unit of product B requires 2 hours on first machine and 1 hour on second machine. Each unit of product A is sold at ₹7 profit and that of product B at a profit of ₹4. A LPP to maximise the profit is:

2026: 14 May Shift 2

In a linear programming problem, the corner points of the feasible region, determined by the system of linear inequalities are (0, 0), (5, 0), (3, 4) and (0, 5). Let $z=5x+qy, q>0$ be the objective function. For what value of q the maximum value of z occurs at both (3, 4) and (0, 5)?

2025: 21 May Shift 2

About linear programming problem (LPP), which of the following statements are correct?

(A) In a LPP, the linear inequalities or restrictions on the variables are called linear constraints.

(B) If the feasible region for an LPP is unbounded, then the maximum or minimum value of the objective function $Z = ax + by$ never exists.

(D) The common region determined by all the linear constraints of an LPP is called the feasible region.

Choose the correct answer from the options given below:

2025: 13 May Shift 1

For the linear programming problem(LPP),

Maximize $Z = 4x + y$

$x + y \leq 5$

$3x + y \leq 9$

$x,y \geq 0$ .

Which of the following are NOT true?

(A) The given LPP has unbounded feasible region.

(B) The corner points of the feasible region are (0,0), (0, 5), (3, 2) and (3, 0).

(D) The given LPP has a unique optimal solution.

Choose the correct answer from the options given below:

The corner points of the bounded feasible region of the LPP: Maximize z=x+yz = x + yz=x+y subject to constraints 2x+5y≤1002x + 5y \leq 1002x+5y≤100, 8x+5y≤2008x + 5y \leq 2008x+5y≤200, x≥0x \geq 0x≥0, y≥0y \geq 0y≥0 are

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CUET Mathematics Past Year Questions (Topic-Wise)

The corner points of the bounded feasible region of the LPP: Maximize $z = x + y$ subject to constraints $2x + 5y \leq 100$ , $8x + 5y \leq 200$ , $x \geq 0$ , $y \geq 0$ are