Minimize the optimum design problem, which is given below, by using graphical method.

$f(x_1,x_2)=(2x_1-5{)}^2+(2x_2-7{)}^2$

Subject to

$-x_1^2+2x_{2}0$

$x_1-2x_2-2$

$2x_{1}5$

$x_{1}0$

$x_{2}0$

Plot and label the constraints and identify the feasible region.

Plot iso$-$cost lines and identify the optimum point.

Identify active constraints at the optimum point; give values of design variables and the cost function at the optimum point $(20$ POINTS$).$