Mathematics Crash Course BITSAT>Chapter 19 - Linear Programming>Exercise 1>Q 31

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The maximum value of $z = 5 x + 2 y,$ subject to the constraints $x + y \leq 7, x + 2 y \leq 10, x, y \geq 0$ is

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Important Questions on Linear Programming

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IMPORTANT

Mathematics Crash Course BITSAT>Chapter 19 - Linear Programming>Exercise 1>Q 32

The maximum value of

P = x + 3 y

such that

2 x + y \leq 20, x + 2 y \leq 20, x \geq 0, y \geq 0

is

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Mathematics

IMPORTANT

Mathematics Crash Course BITSAT>Chapter 19 - Linear Programming>Exercise 1>Q 33

Z = 6 x + 21 y,

subject to

x + 2 y \geq 3, x + 4 y \geq 4, 3 x + y \geq 3, x \geq 0, y \geq 0 .

The minimum value of

Z

occurs at

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Mathematics Crash Course BITSAT>Chapter 19 - Linear Programming>Exercise 1>Q 34

Maximize

Z = 4 x + 6 y,

subject to

3 x + 2 y \leq 12, x + y \geq 4, x, y \geq 0,

is

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Mathematics

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Mathematics Crash Course BITSAT>Chapter 19 - Linear Programming>Exercise 1>Q 35

The maximum value of

P = x + 3 y

, such that

2 x + y \leq 20, x + 2 y \leq 20, x \geq 0, y \geq 0

is

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Mathematics Crash Course BITSAT>Chapter 19 - Linear Programming>Exercise 1>Q 36

Consider $z = - 2 x - 3 y$ subject to $\frac{x}{2} + \frac{y}{3} \leq 1, \frac{x}{3} + \frac{y}{2} \leq 1, x, y \geq 0$ . The maximum value of $z$ is

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Mathematics Crash Course BITSAT>Chapter 19 - Linear Programming>Exercise 1>Q 37

The solution region satisfied by the inequalities

x + y \leq 5, x \leq 4, y \leq 4, x \geq 0, y \geq 0, 5 x + y \geq 5, x + 6 y \geq 6

is bounded by

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Mathematics Crash Course BITSAT>Chapter 19 - Linear Programming>Exercise 1>Q 38

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)

is

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Mathematics Crash Course BITSAT>Chapter 19 - Linear Programming>Exercise 1>Q 39

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