Linear Programming: CBSE Class 12 Previous Year Questions

The feasible region of a linear programming problem with objective function $Z=5x+7y$ is shown below :
The maximum value of Z – minimum value of Z is

1. (A)8
2. (B)29
3. (C)35
4. (D)43

The degree of an objective function of a linear programming problem is

1. (A)0
2. (B)1
3. (C)2
4. (D)Any natural number

In a linear programming problem, the linear function which has to be maximized or minimized is called

1. (A)a feasible function
2. (B)an objective function
3. (C)an optimal function
4. (D)a constraint

For the feasible region shown below, the non-trivial constraints of the linear programming problem are

1. (A)$x+y\le 5$, $x+3y\le 9$
2. (B)$x+y\le 5$, $x+3y\ge 9$
3. (C)$x+y\ge 5$, $x+3y\le 9$
4. (D)$x+y\ge 5$, $3x+y\le 9$

The region represented by the system of inequations $3x+y\ge 3$, $2x-y\ge -5$, $x,y\ge 0$ is :

1. (A)unbounded in 1${}^{st}$ quadrant
2. (B)bounded in 1${}^{st}$ quadrant
3. (C)unbounded in 2${}^{nd}$ quadrant
4. (D)bounded in 2${}^{nd}$ quadrant

In the graph, the feasible region representing the Linear Programming Problem for maximising objective function $Z=px+qy$, $p,q>0$ is shaded. If all points on segment AB give max (Z), then which of the following is true ?

1. (A)$p=2q$
2. (B)$p=3q$
3. (C)$q=3p$
4. (D)$q=2p$

The corner points of the feasible region determined by the system of linear constraints are (0, 0), (0, 40), (20, 40) (60, 20) and (60, 0). If the objective function of an LPP is $Z=4x+3y$, then the maximum value is :

1. (A)200
2. (B)300
3. (C)240
4. (D)120

Assertion (A): Consider a Linear Programming Problem with minimise $Z=x+2y$ subject to constraints $2x+y\ge 3$, $x+2y\ge 6$, $x,y\ge 0$ which gives minimum Z at infinitely many points. The corner points of feasible region are (0, 3) and (6, 0).
Reason (R): If two corner points produce the same minimum value of the objective function, then every point on the line segment joining the points will give the same minimum value.

1. (A)Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A).
2. (B)Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A).
3. (C)Assertion (A) is true, but Reason (R) is false.
4. (D)Assertion (A) is false, but Reason (R) is true.

Solve the following linear programming problem graphically :
Minimize $Z=13x-15y$
Subject to constraints
$x+y\le 7,$
$2x-3y+6\ge 0,$
$x\ge 0,y\ge 0$

Solve the following Linear Programming Problem graphically :
Maximize $Z=\frac{2x}{5}+\frac{3y}{10}$
subject to constraints
$2x+y\le 1000$
$x+y\le 800$
$x,y\ge 0$.