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 :
|
Required |
Chair |
Table |
Available quantity |
|
Wood |
3 |
5 |
150 |
|
Labour |
1 |
2 |
56 |
The number of chairs and tables in appropriate units to be manufactured for maximum profit are, respectively:
Answer & explanation
Correct answer: option 2
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.