OPTIMIZATION doubt !!

[Anjali]

Consider the problem Max.f(x,y)=2x^3−3y^2  subject to (3−x)^3−y^3=0
(a) Solution does not exist   (b) Solution involves complex number (c) Multiple solutions exist  
(d) Solution is x =3,y=0

Iam getting B . Please confirm .

[Anjali]

Plz guide people !!

[Amit Goyal]

Consider the problem Max.f(x,y)=2x^3−3y^2  subject to (3−x)^3−y^3=0
(a) Solution does not exist  
(b) Solution involves complex number
(c) Multiple solutions exist  
(d) Solution is x = 3, y = 0

Max f(x,y) = 2x^3 − 3y^2  subject to (3−x)^3−y^3=0

For the above problem, solution does not exist.
Explanation: The constraint can be re-written as:  x + y = 3. If we substitute in the objective we get:
Max 2x^3 - 3(3-x)^2
Clearly as x goes to infinity the objective tends to infinity.