For the following LPP, maximise $Z=3 x+4 y$ subject to constraints $x-y \geq-1, x \leq 3, x \geq 0, y \geq 0$ the maximum value is
View full solution →Question types
Linear Programming question types
261 questions across 6 question groups — pick any mix to generate a MATHS paper with step-by-step answer keys.
261
Questions
6
Question groups
5
Question types
01
M.C.Q (1 Marks)
228 Q→023 Marks Question
5 Q→035 Marks Questions
10 Q→04Fill In The Blanks[1 Marks ]
6 Q→05True False[1 Marks ]
5 Q→06Answer the question [ 4 mark question ]
7 Q→Sample Questions
Linear Programming questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
The feasible region of an LPP is given in the following figure
Then, the constraints of the LPP are $x \geq 0, y \geq 0$ and
View full solution →Then, the constraints of the LPP are $x \geq 0, y \geq 0$ and
In a linear programming problem, the constraints on the decision variables $x$ and $y$ are $x-3 y \geq 0, y \geq 0$, $0 \leq x \leq 3$. The feasible region
View full solution →In the given graph, the feasible region for a LPP is shaded. The objective function $Z=2 x-3 y$, will be minimum at
View full solution →Based on the given shaded region as the feasible region in the graph, at which point(s) is the objective function $Z=3 x+9 y$ maximum?
View full solution →Solve the Linear Programming Problem graphically:
Minimize Z = -3x + 4y subject to $x + 2y \leq 8, \ 3x + 2y \leq 12, \ x \geq 0, \ y \geq 0.$
View full solution →Minimize Z = -3x + 4y subject to $x + 2y \leq 8, \ 3x + 2y \leq 12, \ x \geq 0, \ y \geq 0.$
Show that the minimum of Z occurs at more than two points.
Maximize Z = x + y, subject to $x - y \leq - 1, - x + y \leq 0, \ x, \ y \geq 0$.
View full solution →Maximize Z = x + y, subject to $x - y \leq - 1, - x + y \leq 0, \ x, \ y \geq 0$.
Solve the Linear Programming Problem graphically:
Maximise Z = 3x + 4y subject to the constraints: $x + y \le4, \ x \geq 0, \ y \geq 0$
View full solution →Maximise Z = 3x + 4y subject to the constraints: $x + y \le4, \ x \geq 0, \ y \geq 0$
Solve the following linear programming problem graphically:
Minimise Z = 200x + 500y subject to the constraints:
$x + 2 y \geq 10$
$3 x + 4 y \leq 24$
$x \geq 0 , y \geq 0$
View full solution →Minimise Z = 200x + 500y subject to the constraints:
$x + 2 y \geq 10$
$3 x + 4 y \leq 24$
$x \geq 0 , y \geq 0$
Solve the following linear programming problem graphically:
Maximise Z = 4x + y subject to the constraints:
x + y $\le$ 50
3x + y $\le$ 90
x $\ge$ 0, y $\ge$ 0
View full solution →Maximise Z = 4x + y subject to the constraints:
x + y $\le$ 50
3x + y $\le$ 90
x $\ge$ 0, y $\ge$ 0
Show that the minimum of Z occurs at more than two points.
Maximize Z = -x + 2y subject to the constraints: $x \geq 3,x + y \geq 5,x + 2y \geq 6,y \geq 0$.
View full solution →Maximize Z = -x + 2y subject to the constraints: $x \geq 3,x + y \geq 5,x + 2y \geq 6,y \geq 0$.
Show that the minimum of Z occurs at more than two points.
Minimise and Maximise Z = x + 2y subject to $x + 2 y \geq 100,2 x - y \leq 0,2 x + y \leq 200$; $x , \ y \geq 0$.
View full solution →Minimise and Maximise Z = x + 2y subject to $x + 2 y \geq 100,2 x - y \leq 0,2 x + y \leq 200$; $x , \ y \geq 0$.
Show that the minimum of Z occurs at more than two points.
Minimize and Maximize Z = 5x + 10y subject to $x + 2y \leq 120, \ x + y \geq 60$, $x - 2y \geq 0, \ x, \ y \geq 0$.
View full solution →Minimize and Maximize Z = 5x + 10y subject to $x + 2y \leq 120, \ x + y \geq 60$, $x - 2y \geq 0, \ x, \ y \geq 0$.
Solve the Linear Programming Problem graphically:
Minimise Z = x + 2y subject to 2x + y $\ge$ 3, x + 2y $\ge$ 6, x, y $\ge$ 0.
View full solution →Minimise Z = x + 2y subject to 2x + y $\ge$ 3, x + 2y $\ge$ 6, x, y $\ge$ 0.
Solve the Linear Programming Problem graphically:
Maximize Z = 3x + 2y subject to $x + 2y \leq 10,3x + y \leq 15,x,y \geq0$
View full solution →Maximize Z = 3x + 2y subject to $x + 2y \leq 10,3x + y \leq 15,x,y \geq0$
Fill in the blanks.
A corner point of a feasible region is a point in the region which is the _________ of two boundary lines.
A corner point of a feasible region is a point in the region which is the _________ of two boundary lines.
Fill in the blanks.
If the feasible region for a LPP is _________, then the optimal value of the objective function Z = ax + by may or may not exist.
If the feasible region for a LPP is _________, then the optimal value of the objective function Z = ax + by may or may not exist.
Fill in the blanks.
In a LPP if the objective function Z = ax + by has the same maximum value on two corner points of the feasible region, then every point on the line segment joining these two points give the same _________ value.
In a LPP if the objective function Z = ax + by has the same maximum value on two corner points of the feasible region, then every point on the line segment joining these two points give the same _________ value.
Fill in the blanks.
A feasible region of a system of linear inequalities is said to be _________, if it can be enclosed within a circle.
A feasible region of a system of linear inequalities is said to be _________, if it can be enclosed within a circle.
Fill in the blanks.
In a LPP, the linear inequalities or restrictions on the variables are called _________.
In a LPP, the linear inequalities or restrictions on the variables are called _________.
State whether the statements are True or False:
In a LPP, the maximum value of the objective function Z = ax + by is always finite.
In a LPP, the maximum value of the objective function Z = ax + by is always finite.
State whether the statements are True or False:
Maximum value of the objective function Z = ax + by in a LPP always occurs at only one corner point of the feasible region.
Maximum value of the objective function Z = ax + by in a LPP always occurs at only one corner point of the feasible region.
Fill in the blanks.
The feasible region for an LPP is always a _________ polygon.
The feasible region for an LPP is always a _________ polygon.
State whether the statements are True or False:
If the feasible region for a LPP is unbounded, maximum or minimum of the objective function Z = ax + by may or may not exist.
If the feasible region for a LPP is unbounded, maximum or minimum of the objective function Z = ax + by may or may not exist.
State whether the statements are True or False:
In a LPP, the minimum value of the objective function Z = ax + by is always 0 if origin is one of the corner point of the feasible region.
In a LPP, the minimum value of the objective function Z = ax + by is always 0 if origin is one of the corner point of the feasible region.
Maximize $Z=3 x+2 y$ subject to constraints $x+2 y \leq 10,3 x+y \leq 15, x \geq 0, y \geq 0$ by using graphical method.
View full solution →Maximise $z=3 x+5 y$ subject to the constraints -
$\begin{array}{l}3 x+5 y \leq 15 \\5 x+2 y \leq 10 \\x \geq 0, y \geq 0\end{array}$
View full solution →$\begin{array}{l}3 x+5 y \leq 15 \\5 x+2 y \leq 10 \\x \geq 0, y \geq 0\end{array}$
Maximise $z=4 x+y$ subject to the constraints -
$\begin{array}{l}x+y \leq 50 \\3 x+y \leq 20 \\x \geq 0, y \geq 0\end{array}$
View full solution →$\begin{array}{l}x+y \leq 50 \\3 x+y \leq 20 \\x \geq 0, y \geq 0\end{array}$
Solve the following linear programming problem for minimisation by graphical method :
Objective function
$
\begin{aligned}Z = 5 x + y \\
constraints
3 x + 5 y & \geq 1 5 \\
5 x + 2 y & \leq 1 0 \\
x \geq 0 , y & \geq 0
\end{aligned}
$
View full solution →Objective function
$
\begin{aligned}Z = 5 x + y \\
constraints
3 x + 5 y & \geq 1 5 \\
5 x + 2 y & \leq 1 0 \\
x \geq 0 , y & \geq 0
\end{aligned}
$
Solve the following linear programming problem by graphical method. Under the following constraints :
$
\begin{aligned}
x+2 y & \geq 10 \\
x+y & \geq 6 \\
3 x+y & \geq 8 \\
x, y & \geq 0
\end{aligned}
$
$\operatorname{minimise} Z=3 x+5 y$.
View full solution →$
\begin{aligned}
x+2 y & \geq 10 \\
x+y & \geq 6 \\
3 x+y & \geq 8 \\
x, y & \geq 0
\end{aligned}
$
$\operatorname{minimise} Z=3 x+5 y$.
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