For L. P. P, maximize z = 4 x 1 + 2 x 2 subject to 3 x 1 + 2 x 2 ≥ 9 , x 1 - x 2 ≤ 3 , x 1 ≥ 0 , x 2 ≥ 0 has ….

Infinite number of optimal solutions

The objective function Z = 4 x 1 + 5 x 2 , subject to 2 x 1 + x 2 ≥ 7 , 2 x 1 + 3 x 2 ≤ 15 , x 2 ≤ 3 & x 1 , x 2 ≥ 0 has minimum value at the point

On the line parallel to x − axis

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The objective function $z = 4 x + 3 y$ can be maximized, subject to the constraints $3 x + 4 y \leq 24,$ $8 x + 6 y \leq 48$ and $x, y \geq 0$

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Important Questions on Linear Programming

MEDIUM

Mathematics>Algebra>Linear Programming>Solution of Linear Programming Problems

The minimum value of

z = 2 x_{1} + 3 x_{2}

z = 2 x_{1} + 3 x_{2}

subject to the constraints

2 x_{1} + 7 x_{2} \geq 22

x_{1} + x_{2} \geq 6, 5 x_{1} + x_{2} \geq 10

and

x_{1}, x_{2} \geq 0

HARD

Mathematics>Algebra>Linear Programming>Solution of Linear Programming Problems

Z = 7 x + y

subject to

5 x + y \geq 5, x + y \geq 3, x \geq 0, y \geq 0,

then the minimum value of

Z

EASY

Mathematics>Algebra>Linear Programming>Solution of Linear Programming Problems

The most correct statement is

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Mathematics>Algebra>Linear Programming>Solution of Linear Programming Problems

The corner points of the feasible region determined by the system of linear constraints are

(0, 10), (5, 5), (25, 20)

and

(0, 30) .

Let

Z = p x + q y,

where

p, q > 0 .

Condition on

p

and

q

so that the maximum of

Z

occurs at both the points

(25, 20)

and

(0, 30)

is _________.

EASY

Mathematics>Algebra>Linear Programming>Solution of Linear Programming Problems

The coordinates of the point at which minimum value of

Z = 7 x - 8 y

subject to constraints

x + y - 20 \leq 0,

y \geq 5,

x \geq 0,

y \geq 0

is attained, is

EASY

Mathematics>Algebra>Linear Programming>Solution of Linear Programming Problems

For the

LPP

; maximize

z = x + 4 y

subject to the constraints

x + 2 y \leq 2, x + 2 y \geq 8, x, y \geq 0

MEDIUM

Mathematics>Algebra>Linear Programming>Solution of Linear Programming Problems

The feasible region of an LPP is shown in the figure. If

Z = 11 x + 7 y

, then the maximum value of

Z

occurs at

Question Image

MEDIUM

Mathematics>Algebra>Linear Programming>Solution of Linear Programming Problems

The shaded region is the solution set of the inequalities

Question Image

HARD

Mathematics>Algebra>Linear Programming>Solution of Linear Programming Problems

The maximum value of

z = 9 x + 13 y

subject to constraints

2 x + 3 y \leq 18, 2 x + y \leq 10, x \geq 0, y \geq 0

EASY

Mathematics>Algebra>Linear Programming>Solution of Linear Programming Problems

The maximum value of

Z = 4 x + 2 y

subject to constraints

2 x + 3 y \leq 18, x + y \geq 10

and

x, y \geq 0

EASY

Mathematics>Algebra>Linear Programming>Solution of Linear Programming Problems

The corner points of the feasible region determined by the system of linear constraints are

(0, 10), (5, 5), (15, 15), (0, 20) .

Let

Z = p x + q y

where

p, q > 0

. Condition on

p

and

q

so that the maximum of

z

occurs at both the points

(15, 15)

and

(0, 20)

, is

HARD

Mathematics>Algebra>Linear Programming>Solution of Linear Programming Problems

The maximum value of $z = 6 x + 8 y$ subject to $x - y \geq 0, x + 3 y \leq 12, x \geq 0, y \geq 0$ is

HARD

Mathematics>Algebra>Linear Programming>Solution of Linear Programming Problems

The minimum value of the function

Z = 2 x - y

, subjected to the constraints

x + y \leq 5, x + 2 y \geq 8, x \geq 0, y \geq 0

, is

EASY

Mathematics>Algebra>Linear Programming>Solution of Linear Programming Problems

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

Question Image

MEDIUM

Mathematics>Algebra>Linear Programming>Solution of Linear Programming Problems

Consider a Linear Programming Problem:
Minimize

Z = 5 x + 3 y

Subject to :

3 x + y \geq 10, 2 x + 2 y \geq 14

and

x + 2 y \geq 9 .

Which one of the following points lies outside the feasible region?

EASY

Mathematics>Algebra>Linear Programming>Solution of Linear Programming Problems

Solve graphically the following linear programming problem:

Maximize or minimize $Z = x + 2 y$ subject to constraints $x + 2 y \geq 100, 2 x - y \leq 0, 2 x + y \leq 200 & x \geq 0, y \geq 0$ .

HARD

Mathematics>Algebra>Linear Programming>Solution of Linear Programming Problems

A furniture trader deals in only two items - chairs and tables. He has $50, 000$ rupees to invest and a space to store at most $35$ items. A chair costs him $1000$ rupees and a table costs him $2000$ rupees . The trader earns a profit of $150$ rupees and $250$ rupees on a chair and table, respectively. Formulate the above problem as an LPP to maximise the profit and solve it graphically.

MEDIUM

Mathematics>Algebra>Linear Programming>Solution of Linear Programming Problems

Corner points of the feasible region determined by the system of linear constraints are

(0, 3), (1, 1)

and

(3, 0)

. Let

z = p x + q y

, where

p, q > 0

. Condition on

p

and

q

so that the minimum of

z

occurs at

(3, 0)

and

(1, 1)

EASY

Mathematics>Algebra>Linear Programming>Solution of Linear Programming Problems

For L. P. P, maximize

z = 4 x_{1} + 2 x_{2}

subject to

3 x_{1} + 2 x_{2} \geq 9, x_{1} - x_{2} \leq 3, x_{1} \geq 0, x_{2} \geq 0

has ….

HARD

Mathematics>Algebra>Linear Programming>Solution of Linear Programming Problems

The objective function

Z = 4 x_{1} + 5 x_{2},

subject to

2 x_{1} + x_{2} \geq 7, 2 x_{1} + 3 x_{2} \leq 15, x_{2} \leq 3 & x_{1}, x_{2} \geq 0

has minimum value at the point

The objective function z=4x+3y can be maximized, subject to the constraints 3x+4y≤24, 8x+6y≤48 and x, y≥0

Important Questions on Linear Programming

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The objective function $z = 4 x + 3 y$ can be maximized, subject to the constraints $3 x + 4 y \leq 24,$ $8 x + 6 y \leq 48$ and $x, y \geq 0$