A carpenter earns a profit of ₹50 and ₹80 on one chair and one table respectively. The requirement and availability of wood and labour are tabled as :

The number of chairs and tables in appropriate units to be manufactured for maximum profit are, respectively:

50, 0

The correct answer is Option (2) - 50, 0

$\text{Let chairs } = x,\;\; \text{tables } = y$

$\text{Maximise } Z = 50x + 80y$

$3x + 5y \le 150$

$x + 2y \le 56$

$x, y \ge 0$

$3x + 5y = 150,\;\; x + 2y = 56$

$x = 56 - 2y$

$3(56 - 2y) + 5y = 150$

$168 - 6y + 5y = 150$

$168 - y = 150$

$y = 18$

$x = 56 - 36 = 20$

$Z(20,18) = 50(20) + 80(18) = 1000 + 1440 = 2440$

$Z(50,0) = 2500,\;\; Z(0,28) = 2240$

$\text{Maximum occurs at } (50,0)$

The required numbers are $50$ chairs and $0$ tables.