Problem $4(20)$

Consider the following nonlinear program,

min,$e^{(x_1+x_2+x_3)}+(x_1{)}^2+(x_2{)}^2+(x_3{)}^2-x_1+x_2$

$s.t.(x_1-2{)}^2+(x_2-3{)}^{2}3$

$,x_1+x_2+3x_3=5$

$,x_1,x_2,x_3$inR

The optimal solution is found at $x_1=0\mathrm{.}882,x_2=1\mathrm{.}677,x_3=0\mathrm{.}814$ with an optimal objective function value of $34\mathrm{.}206.$ Use sensitivity analysis to predict what is the value of the objective function if the constraint $(x_1-2{)}^2+(x_2-3{)}^{2}3$ changes to $(x_1-2{)}^2+(x_2-3{)}^{2}3\mathrm{.}1.$ Justify.