Question $8[8]$

Consider the following NLP:

Minimise

$f(x,y)=x^2+y^2-6x-14y$

subject to the constraints

$x+y2,$

$x+2y3.$

Solve the NLP problem by considering the following cases only, case$-$one: ${}_1=0={}_2$

and case$-$two: ${}_1=0$ and ${}_{2}0$; in each case state whether you accept or reject the

obtained solution and use the given constraints to justify your decision.