List of top Mathematics Questions on Linear Programmig Problem asked in CUET (UG)

In a Linear Programming Problem (LPP), if the objective function to maximize is \( Z = 3x + 4y \) and the corner points of the feasible bounded region are \( (0,0), (4,0), (2,3), \) and \( (0,4) \), find the maximum value of \( Z \).

For the L.P.P. Maximize \[ z=10x+6y \] subjected to: \[ 3x+y\leq12 \] \[ 2x+5y\leq34 \] \[ x,y\geq0 \] Then the feasible region represented by system of inequalities is:

The corner points of the feasible region determined by $x + y \leq 8$, $2x + y \geq 8$, $x \geq 0$, $y \geq 0$ 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:

Which one of the following represents the correct feasible region determined by the following constraints of an LPP?
\[ x + y \geq 10, \quad 2x + 2y \leq 25, \quad x \geq 0, \quad y \geq 0 \]

The corner points of feasible region determined by the system of linear constraints are (0, 3), (1, 1) and (3, 0). Let Z = px + qy where p, q > 0. The condition on p and q so that, minimum of Z occurs at (3, 0) and (1, 1) is :

Which of the following is correct ?

For x+y=8, the maximum value of xy is:

The maximum value of Z=5x+3y subject to the constraints \(2x+4y \leq16,\) \(3x+y\leq9\). \(x,y\geq0\) is:

Match List I with List II

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The maximum value of Z= 2x + 3y subject to the constraints x≥0, y>0; x+y≤ 10, 3x+4y≤ 36 is:

If the objective function for an LPP is \( z=3x-4y \) and corner points for bounded feasible region are \((5, 0) (6, 5) \)and \((4, 10)\), then:
(A) maximum value of \(z\) is \(2\)
(B)minimum value of\( z\) is \(2\)
(C) maximum value of \(z \)is at \((5, 0)\)
(D) no maximum value of\( z\)
(E)maximum value of \(z\) is \(15\)
Choose the correct answer from the options given below:

Which of the following statements is true ?
A. If the feasible region for a LPP is unbounded, maximum or minimum of the objective function Z = ax + by may or may not exist.
B. Maximum value of the objective function Z = ax + by in a LPP always occurs at only one corner point of the feasible region.
C. In a LPP, the minimum value of the objective function Z = ax + by (a, b > 0) is always 0 if origin is one of the corner points of feasible region.
D. In a LPP the max value of the objective function Z = ax + by is always finite.
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The minimum value of z=3x+6y subject to the constraints \(2x+3y≤180\), \(x+y≥60\), \(x≥3y\), \(x≥0\), \(y≥0\) is:

Match LIST I with LIST II

List-I		List-II
A	If the corner points of the feasible region For an LPP are (0, 4), (5, 0), (7, 9), then the minimum value of the objective function Z =5x+y is.	I	27
B	If the corner points of the feasible region for an LPP are (0, 0), (0, 2), (3, 4), (5, 3). then the maximum value of the objective function Z=3x+4y	II	60
C	The comer points of the feasible region for an LPP are (0, 2), (1, 2), (4,3), (7, 0). The objective function is Z = x+5y. Then (Max Z+Min Z) is	III	25
D	If the corner points of the feasible region for an LPP are (0, 4), (3, 0), (3, 2), (6,9) The objective function is Z=2x+6y. Then (Max Z-Min Z)	IV	26

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The feasible region of an LPP is shown in the figure below.
If \( z=3x+9y\), then the minimum value of \(z\) occurs at :

Objective function \(z=30x-30y \) is subject to which combination of constraints, with feasible solution shown in the figure.

(A)\(x \geq 0, \quad y \geq 0, \quad x \leq 15\)
(B)\(y \leq 20, \quad x + y \leq 30\)
(C)\(x + y \leq 30, \quad x + y \leq 15, \quad 2x - y \leq 5\)
(D)\(2x + y \leq 30, \quad x + y \leq 15, \quad x > 15\)
(E)\(3x + y \leq 30, \quad x + 3y \leq 15, \quad y \geq 20\)
Choose the correct answer from the options given below:
 

Match List I with List II

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The maximum value of Z = 3x + 4y subject to constraint x + y ≤6, x, y ≥ 0 is:

For the LPP, Min \(Z= 5x + 7y\) subject to \(x≥0, y≥0; 2x+y≥8, x+2y≥ 10,\) the basic feasible solutions are:

Consider the following feasible region. Which of the following constraints represents the feasible region ?

A. 2x + 3y ≤ 6
B. x - 2y ≤ 2
C. 3x + 2y ≤ 12
D. 3x - 2y ≤ -3
E. x - 2y ≥ -1
Choose the correct answer from the options given below :

Match List I with List II

List I	List II
A. The region represented by \(x \geq 0, y \geq 0\)	I. no feasible region
B. The region represented by the inequalities \(2x + y \geq 3, x + 2y \geq 6, x,y \geq 0\)	II. 1st quadrant
C. The region represented by the inequalities \(x + 2y \leq 8, 3x + 2y \leq 12, x,y \geq 0\)	III. unbounded
D. The region represented by the inequalities \(x + y \leq 2, 3x + 5y \geq 15, x,y \geq 0\)	IV. bounded

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If corner points of a feasible region are (0, 0), (2,0) \((\frac{20}{19},\frac{45}{19})\) and (0, 3), then
(A) Maximum value of z=5x+3y is 10
(B) Minimum value of z=5x+3y is 0
(C) Maximum value of z=5x+3y is \(\frac{235}{19}\) and minimum value is 0
(D) Maximum value of z=5x+3y is 10 and minimum value is 0
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The value of objective function is maximum under linear constraints is

The corner points of the feasible region determined by the system of linear inequalities are (0, 0), (0, 4), (4, 0), (2, 4) and (0, 5). If the maximum value of Z = ax + by where a, b > 0 occurs at both (2, 4) and (4, 0) then