Q$3.$ Now we are going to one step further and try to solve a constrained optimization problem for two variables.

$f(x,y)y^3$

min

$s.t.x^2+4y^{2}24$

$x+y0$

$[4$ marks$]$

Here, $$ is a random variable between $-1$ and $1.$

The program should be able to solve the above constrained problem. It should also figure out whether the constrained is active or not based on the value of the Lagrange multiplier.

If the program find out that one of the constrained is not active, then it should again need to find the optimum value with updated information about active constraints.

Generate a plot showing the both the constraints and the optimum value marked on it$.$ This will help you understand active and inactive constraints.

Note: Although you are not writing the most generic program for the constrained optimization, it should give some idea regarding it$.$ python coding compulsory