A carpenter makes chairs and tables. A chair needs 2 hours on the machine and 1 hour of hand finishing. A table needs 1 hour on the machine and 2 hours of hand finishing. At most 40 machine hours and 50 hours of hand finishing are available in a week. The profit is Rs. 30 on a chair and Rs. 40 on a table. The maximum weekly profit is
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → Rs. 1100
Let x chairs and y tables be made in a week. Then the problem is:
Maximise \(Z = 30x + 40y\)
subject to \(2x + y \le 40\), \(x + 2y \le 50\), \(x, y \ge 0\)
The two lines meet where, putting \(y = 40 - 2x\),
\(x + 80 - 4x = 50\)
\(x = 10, \; y = 20\)
The bounded region has corner points (0, 0), (20, 0), (10, 20) and (0, 25). Values of Z:
\(Z(0, 0) = 0\)
\(Z(20, 0) = 600\)
\(Z(10, 20) = 300 + 800 = 1100\)
\(Z(0, 25) = 1000\)
The maximum weekly profit is Rs. 1100, from 10 chairs and 20 tables.