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Linear Inequalities

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Question : 52 of 54

Marks: +1, -0

A manufacturer produces two items A and B. He has Rs.10,000 to invest and a space to store 100 items. A table costs him Rs. 400 and a chair Rs.100. Express this in the form of linear inequalities.

$x+y \leq 100,4 x+y \leq 100, x \geq 0, y \geq 0$
$x+y \leq 1000,2 x+5 y < 1000, x \geq 0, y \geq 0$
$x+y > 100,4 x+y \geq 100, x \geq 0, y \geq 0$
none of these

Solution:

Concept:

Define variables for number of tables (x) and chairs (y) and translate cost and space limits into inequalities.

Explanation:

Let

x

be the number of tables and

y

be the number of chairs.

Cost constraint:

400x + 100y \leq 10000

. Divide by 100:

4x + y \leq 100

.

Space constraint:

x + y \leq 100

.

Non‑negativity:

x \geq 0

,

y \geq 0

.

Answer:

x+y \leq 100

,

4x+y \leq 100

,

x \geq 0

,

y \geq 0

which matches option A.

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