Q. Find the feasible solution of inequations 3x+2y$\le$18, 2x+y$\le$10, x$\ge$0, y$\ge$0.

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Please find below the solution to the asked query:

$$\begin{gathered} 3\mathrm{x}+2\mathrm{y}\le 18 \\ \mathrm{If} \mathrm{we} \mathrm{plot} \\ 3\mathrm{x}+2\mathrm{y}=18 \\ \Rightarrow \frac{\mathrm{x}}{6}+\frac{\mathrm{y}}{9}=1 \mathrm{which} \mathrm{means} \mathrm{line} \mathrm{will} \mathrm{meet} \mathrm{x}-\mathrm{axis} \left(6,0\right) \mathrm{and} \mathrm{y}-\mathrm{axis} \mathrm{at} \left(0,9\right) \\ 2\mathrm{x}+\mathrm{y}\le 10 \\ \mathrm{If} \mathrm{we} \mathrm{plot} \\ 2\mathrm{x}+\mathrm{y}=10 \\ \Rightarrow \frac{\mathrm{x}}{5}+\frac{\mathrm{y}}{10}=1 \mathrm{which} \mathrm{means} \mathrm{line} \mathrm{will} \mathrm{meet} \mathrm{x}-\mathrm{axis} \left(5,0\right) \mathrm{and} \mathrm{y}-\mathrm{axis} \mathrm{at} \left(0,10\right) \\ \mathrm{x}\ge 0 \mathrm{and} \mathrm{y}\ge 0 \mathrm{means} \mathrm{we} \mathrm{are} \mathrm{concerned} \mathrm{with} \mathrm{first} \mathrm{quadrant} \mathrm{only}. \end{gathered}$$


Polygon OBADO is feasible region.

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