Linear Programming - CBSE STD 12 Science Mathematics Questions

Q 1M.C.Q (1 Marks)1 Mark

In the feasible region, any point which given the optimal value (maximum or minimum) of the objective function, is called :

✓
optimal solution
B
inconsistent solution
C
feasible solution
D
anomalous solution.

Answer: A.

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Q 2M.C.Q (1 Marks)1 Mark

Any point of the outer part of feasible region is called :

A
feasible solution
✓
inconsistent solution
C
consistent solution
D
anomalous solution.

Answer: B.

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Q 3M.C.Q (1 Marks)1 Mark

The maximum solution of the objective function lies :

A
in feasible region
✓
at the corner of the feasible region
C
has no feasible region
D
none of the above.

Answer: B.

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Q 4M.C.Q (1 Marks)1 Mark

The feasible region is :

A
always concave polygon
B
always quadrilateral
✓
always convex polygon
D
none of the above.

Answer: C.

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Q 51 Marks Question1 Mark

Show the feasible region of the constraints $3 x+5 y \leq 15, x \geq 0, y \geq 0$.

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Q 61 Marks Question1 Mark

Show the feasible region of the constraints $2 x+y \leq 4$, $x \geq 0, y \geq 0$.

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Q 71 Marks Question1 Mark

Show the feasible region under the constraints $x+y \leq$ $4, x \geq 0, y \geq 0$.

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Q 81 Marks Question1 Mark

Define linear objective function.

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Q 91 Marks Question1 Mark

What are optimal feasible problems?

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Q 102 Marks Questions2 Marks

Show the feasible region of the constraints $4 x+5 y \geq$ $20, x \geq 0, y \geq 0$.

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Q 112 Marks Questions2 Marks

Show the feasible region of the constraints $\frac{x}{3}+\frac{y}{4} \geq 1, x \geq 0, y \geq 0$.

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Q 122 Marks Questions2 Marks

Show the feasible region of the constraints $2 x+3 y \leq 6$, $x \geq 0, y \geq 0$.

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Q 132 Marks Questions2 Marks

Show the feasible region under the constraints :
$
\begin{aligned}
2 x+y & \leq 6 \\
x & \geq 0 \\
y & \geq 0
\end{aligned}
$

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Q 142 Marks Questions2 Marks

Show the feasible solution region under the following constraints: $ 8 x+5 y \leq 40, x \geq 0, y \geq 0 .$

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Q 155 Marks Questions5 Marks

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.

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Q 165 Marks Questions5 Marks

Maximize $Z=4 x+y$ subject to constraints $x+y$ $\leq 50,3 x+y \leq 90, x \geq 0, y \geq 0$ by using graphical method.

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Q 175 Marks Questions5 Marks

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}
$

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Q 185 Marks Questions5 Marks

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}
$
$\operatorname{minimise} Z=3 x+5 y$.

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Q 195 Marks Questions5 Marks

Solve the following linear programming problem by graphical method.Under the constraints, maximise $Z=60 x+40 y$.
$
\begin{aligned}
x+2 y & \leq 12 \\
2 x+y & \leq 12 \\
x+\frac{5}{4} y & \geq 5 ; x \geq 0, y \geq 0
\end{aligned}
$

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Q 20Fill In The Blanks[1 Marks ]1 Mark

At the corner point $(15,15)$ the corresponding value of Z will ___________ if $Z =3 x+9 y$.

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Q 21Fill In The Blanks[1 Marks ]1 Mark

Any point of the feasible region which given the optimal value (maximum or minimum value) of the objective function is called __________ .

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Q 22Fill In The Blanks[1 Marks ]1 Mark

Any point of the external part of the feasible region is called ___________ .

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Q 23Fill In The Blanks[1 Marks ]1 Mark

Feasible region is always __________ .