question_answer

Two farmers Hariom and Siyaram cultivates only three varieties of rice namely Basmati, Permal and Naura. The sale (in Rs.) of these varieties of rice by both the farmers in the month of September and October are given by the following matrices A and B. September Sales (in Rs.)                  Basmati Permal Naura \[\begin{align}   & \text{Basmati}\,\,\,\,\,\,\,\text{Parmal}\,\,\,\,\,\,\,\text{Naura} \\  & A=\left[ \begin{matrix}    10000 & 20000 & 30000  \\    50000 & 30000 & 10000  \\ \end{matrix} \right]\begin{matrix}    \text{Hariom}  \\    \text{siyaram}  \\ \end{matrix} \\ \end{align}\] October Sales (in Rs.) \[\begin{align}   & \text{Basmati}\,\,\,\,\,\,\,\text{Parmal}\,\,\,\,\,\,\,\text{Naura} \\  & B=\left[ \begin{matrix}    5000 & 10000 & 6000  \\    20000 & 10000 & 10000  \\ \end{matrix} \right]\begin{matrix}    \text{Hariom}  \\    \text{siyaram}  \\ \end{matrix} \\ \end{align}\] (i) Find the combined sales in September and October for each farmer in each variety. (ii) Find the decrease in sales from September to October. (iii) If both farmers receive 2% profit on gross sales, then compute the profit for each farmer and for each variety sold in October. Which variety of rice preferred the most and why?

Answer:

(i) Combined sales in September and October for each farmer in each variety is given by             (ii) Change in sales from September to October is given by (iii) Required profit = 2% of October sales             \[=\frac{2}{100}\times B=0.02\times B\] Thus, in October, Hariom receives Rs. 100, Rs. 200 and Rs.120 as profit in the sale of each variety of rice, respectively and Siyaram receives profit of Rs. 400, Rs. 200 and Rs. 200 in the sale of each variety of rice, respectively.                                 Value Since, the sale of Basmati rice in both months is high, as compared to other varieties, therefore Basmati rice preferred the most. This is because Basmati rice are tasty and healthy.