CUET UG Mathematics Applied Linear Programming Previous Year Question Paper and Solution with PDF

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CUET UG Mathematics Applied
Previous Year Questions

CUET UG Mathematics Applied
Previous Year Questions
CUET UG Mathematics Applied

CUET UG Mathematics Applied Previous Year Questions (PYQs)

CUET UG Mathematics Applied Linear Programming PYQ

Qus : 1 CUET UG Mathematics Applied PYQ

The maximum value of $z=4x+2y$ subject to constraints

$2x+3y \le 28$,

$x+y \le 10$,

$x,y \ge 0$ is:

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CUET UG Mathematics Applied Previous Year PYQ CUET UG Mathematics Applied CUET UG 2022 Applied Mathematics PYQ

Solution

Corner points of feasible region:

$(0,0)$

From $x+y=10$

If $x=0$, $y=10$ → but check first constraint:

$2(0)+3(10)=30>28$ ❌ not feasible

So take intersection of

$2x+3y=28$

$x+y=10$

Solve:

$y=10-x$

Substitute:

$2x+3(10-x)=28$

$2x+30-3x=28$

$-x=-2$

$x=2$

Then

$y=10-2=8$

So intersection point $(2,8)$

Now check intercepts:

If $y=0$

From $x+y=10$ → $x=10$

Check first constraint:

$2(10)+0=20\le 28$ ✔

So point $(10,0)$ is feasible.

Now evaluate $z=4x+2y$

At $(0,0)$ → $0$

At $(2,8)$ → $4(2)+2(8)=8+16=24$

At $(10,0)$ → $40$

Maximum value = 40

Qus : 2 CUET UG Mathematics Applied PYQ

Corner points of the feasible region for an LPP are

$(0,2),; (3,0),; (6,0)$ and $(6,8)$.

If $z=2x+3y$ is the objective function of LPP then

$\max(z)-\min(z)$ is equal to:

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CUET UG Mathematics Applied Previous Year PYQ CUET UG Mathematics Applied CUET UG 2022 Applied Mathematics PYQ

Solution

Evaluate $z=2x+3y$ at each corner point:

At $(0,2)$

$z=2(0)+3(2)=6$

At $(3,0)$

$z=2(3)+3(0)=6$

At $(6,0)$

$z=2(6)+0=12$

At $(6,8)$

$z=2(6)+3(8)=12+24=36$

So,

$\max(z)=36$

$\min(z)=6$

Therefore,

$\max(z)-\min(z)=36-6=30$

Qus : 3 CUET UG Mathematics Applied PYQ

The corner points of the feasible region for an L.P.P are

$(2,0),(7,0),(4,5),(0,3)$

and

$z=2x+3y$

is the objective function.

The difference of the maximum and minimum values of $z$ is:

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CUET UG Mathematics Applied Previous Year PYQ CUET UG Mathematics Applied CUET UG 2022 Applied Mathematics PYQ

Solution

Evaluate $z=2x+3y$ at each corner point. At $(2,0)$ $z=2(2)+3(0)=4$ At $(7,0)$ $z=2(7)+3(0)=14$ At $(4,5)$ $z=2(4)+3(5)=8+15=23$ At $(0,3)$ $z=2(0)+3(3)=9$ Maximum value of $z=23$ Minimum value of $z=4$ Difference $23-4=19$

Qus : 4 CUET UG Mathematics Applied PYQ

The corner points of the feasible region determined by x + y ≤ 8, 2x + y ≥ 8, x ≥ 0, y ≥ 0 are A(0, 8), B(4, 0), and C(8, 0). If the objective function Z = ax + by has its maximum value on the line segment AB, then the relation between a and b is:

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CUET UG Mathematics Applied Previous Year PYQ CUET UG Mathematics Applied CUET UG 2024 Mathematics PYQ