Q$\mathrm{.}10.$ Solve the following LPP$.$

MaxZ$=x_1+1\mathrm{.}2x_2$

Subject to $($i$)2x_1+x_{2}180($ii$)x_1+3x_{2}300$ and $x_1,x_{2}0.$

Additionally, determine the impact on the optimal solution when the constant of the right$-$hand side constraint of $($i$)$ changes from $180$ to $181.$ Calculate the corresponding shadow price as well.