Hello everyone, I have to solve a very difficult problem in R.

I have to maximise the function f(x,y) = x^2 +x*y+y^2+3*y+2 and I have two constraints:

- I have to maximise inside the parabola y=x^2-2
- and I have to respect the constraint y<= 1

I would solve it like this, but I don’t know how to write the matrix A and the vector b.

f ← function (xx,y) xx^2 + xx*y +y^2 +3*y +2

f

fv ← function (x) f(x[1],x[2])

fv

xx ← seq (-5,5,len=51)

y ← seq (-5,5,len=51)

z = outer (xx,y,f)

image (xx,y,z)

contour (xx,y,z,add=T)

curve (x^2 -2 ,-5,5,add=T)

abline (h=1)

constrOptim (c(0,0),fv,NULL,A,bcontrol=list (fnscale=-1))

I have the exam on Monday, so please help me this weekend.

Thank you in advance,

good by and sorry for my bad english.