NCERT Class 12 Maths · Chapter 3 Matrices · Miscellaneous Exercise Question 7

✅ Step-by-Step Solution

1. Represent prices by \(\left[\begin{matrix}\frac{5}{2}\\\frac{3}{2}\\1\end{matrix}\right]\) and costs by \(\left[\begin{matrix}2\\1\\\frac{1}{2}\end{matrix}\right]\).
2. Revenue vector = quantity matrix × price vector = \(\left[\begin{matrix}46000\\53000\end{matrix}\right]\).
3. Unit profit vector is \(\left[\begin{matrix}\frac{1}{2}\\\frac{1}{2}\\\frac{1}{2}\end{matrix}\right]\). Multiplying by quantities gives \(\left[\begin{matrix}15000\\17000\end{matrix}\right]\).
4. Hence gross profits are ₹15000 and ₹17000, totalling ₹32000.