Question

A furniture dealer deals in only two items - tables and chairs. He has ₹ 15000 to invest and a space to store atmost 60 pieces. A table costs him ₹ 750 and a chair ₹ 150. Suppose he makes $x$ tables and $y$ chairs.
The above data in the form of inequations can be written as

• A. $750 x+150 y<15000, x+y<60, x \geq 0$ and $y \geq 0$
• B. $750 x+150 y>15000, x+y>60, x \geq 0$ and $y \geq 0$
• C. $750 x+150 y \leq 15000, x+y \leq 60, x \geq 0$ and $y \geq 0$
• D. $750 x+150 y \geq 15000, x+y \geq 60, x \geq 0$ and $y \geq 0$

Answer 1

Answer: (C)

Total cost of $x$ tables and $y$ chairs $=750 x+150 y$
Since, he has $₹ 15000$ to invest, then
$750 x+150 y \leq 15000$
Again, he has space to store at most 60 pieces
$\therefore x+y \leq 60$
$\because x$ and $y$ are numbers, $x \geq 0, y \geq 0$
Hence, linear inequalities representing the above data are
$750 x+150 y \leq 15000, x+y \leq 60, x \geq 0$ and $y \geq 0$