$($a$)$ Consider the following non$-$linear programming problem:

Maximise $f(x_1,x_8)=3x_1+5x_n$

Subject to $x_1,x_{2}8$

$x^2+x^2-10$

$x_{1}0,x_{2}0$

Draw the diagram of the feasible region of the problem. Determine the optimum solution graphically.