Question

Mohan’s fixed commission is ₹560 per assignment. Cost = ₹\(2n^2\), where \(n\) = number of chairs made. If average cost per chair ≤ ₹68, then minimum and maximum values of \(n\) are:

• A. 13 and 19
• B. 13 and 20
• C. 14 and 19
• D. 14 and 20

Hint:

Convert average constraints to inequalities, simplify, and solve quadratic inequalities using factorization or quadratic formula.

Answer 1

The Correct Option is D

Total cost per assignment = ₹\(560 + 2n^2\) Average cost per chair: \[ \frac{560 + 2n^2}{n} \leq 68 \Rightarrow 560 + 2n^2 \leq 68n \Rightarrow 2n^2 - 68n + 560 \leq 0 \Rightarrow n^2 - 34n + 280 \leq 0 \] Solve: \[ n = \frac{34 \pm \sqrt{(-34)^2 - 4 \times 280}}{2} = \frac{34 \pm \sqrt{1156 - 1120}}{2} = \frac{34 \pm \sqrt{36}}{2} = \frac{34 \pm 6}{2} \Rightarrow n = 14 \text{ to } 20 \] So \(n\) must lie between 14 and 20 inclusive.