question_answer

Two farmers Ramkrishna and Gurcharan Singh cultivates only three crops rice, maize and wheat. The sales (in Rs.) of these crops in the month of July and August are given by the following matrices. July sales \[\begin{align}   & \text{Rice}\,\,\,\,\,\,\,\,\text{Maize}\,\,\,\,\,\text{Wheat} \\  & A=\left[ \begin{matrix}    15000 & 10000 & 50000  \\    45000 & 20000 & 25000  \\ \end{matrix} \right]\begin{matrix}    \text{Ramkishan}  \\    \text{Gurcharan}\,\,\text{singh}  \\ \end{matrix} \\ \end{align}\] August sales \[\begin{align}   & \text{Rice}\,\,\,\,\,\,\text{Maize}\,\,\,\,\,\,\,\,\,\text{Wheat} \\  & A=\left[ \begin{matrix}    10000 & 15000 & 20000  \\    15000 & 5000 & 25000  \\ \end{matrix} \right]\begin{matrix}    \text{Ramkishan}  \\    \text{Gurcharan}\,\,\text{singh}  \\ \end{matrix} \\ \end{align}\] (i) Find the combined sales in July and August for each farmer in each crop. (ii) If both farmers receive 1.5% profit on gross sales. Compute the profit for each farmer for crop sold in July. (iii) Give suggestions to the farmers keeping 'Save Environment' in mind.

Answer:

July sales Given, August sales \[B={{\left[ \begin{align}   & \begin{matrix}    10000 & 15000 & 20000  \\ \end{matrix} \\  & \begin{matrix}    15000 & 5000 & 25000  \\ \end{matrix} \\ \end{align} \right]}_{GurcharanSingh}}^{Ramkishan}\] (i) Combined sales in July and August for each farmer in each crop \[A+B=\left[ \begin{align}   & 15000+10000\,\,\,\,10000+15000\,\,\,\,50000+20000 \\  & 45000+15000\,\,\,\,20000+5000\,\,\,\,\,\,25000+25000 \\ \end{align} \right]\]         \[\begin{align}   & \begin{matrix}    \,\,\,\,\,\,\,\,\,\,Rice & \,\,\,Maize & \,\,Wheat  \\ \end{matrix} \\  & =\left[ \begin{align}   & \begin{matrix}    25000 & 25000 & 70000  \\ \end{matrix} \\  & \begin{matrix}    60000 & 25000 & 50000  \\ \end{matrix} \\ \end{align} \right] \\ \end{align}\] (ii) Given both farmers receive 1.5% profit on gross sales. \[\therefore \]Profit of each farmer in July \[=1.5%\] of \[A=\frac{1.5}{100}\times A=0.015\times A\] \[=0.015\left[ \begin{align}   & \begin{matrix}    15000 & 10000 & 50000  \\ \end{matrix} \\  & \begin{matrix}    45000 & 20000 & 25000  \\ \end{matrix} \\ \end{align} \right]\] \[=\left[ \begin{align}   & 15000\times 0.015\,\,\,\,10000\times 0.015\,\,\,\,50000\times 0.015 \\  & 45000\times 0.015\,\,\,\,20000\times 0.015\,\,\,\,25000\times 0.015 \\ \end{align} \right]\]\[={{\left[ \begin{align}   & \begin{matrix}    225 & 150 & 750  \\ \end{matrix} \\  & \begin{matrix}    675 & 300 & 375  \\ \end{matrix} \\ \end{align} \right]}_{Gurcharan\,\,Singh}}^{Ramkishan}\] \[\therefore \]Ramkishan?s profit\[=225+150+750=Rs.\,\,1125\] and Gurcharan Singh?s profit \[=675+300+375=Rs.\,\,1350\] (iii) For saving environment (a) Farmers should use the process of crop-rotation (b) also they should use least amount of fertilisers and least water.