(a) Find all solution candidates for maximising f(x,y,z)=9x^(2)+4y^(2)+z^(2) subject to g(x,y,z)=x^(2)+y^(2)+z^(2) = 0,y >= 0,z >= 0 by forming the relevant Lagrangian, and applying the

(a) Find all solution candidates for maximising f(x,y,z)=9x^(2)+4y^(2)+z^(2) subject to g(x,y,z)=x^(2)+y^(2)+z^(2) <= 1 and x >= 0,y >= 0,z >= 0 by forming the relevant Lagrangian, and applying the first-order conditions (FOCs) and the complementary slackness conditions. For which solution candidates is the main inequality constraint binding, and what is the maximum? (It may be useful to start first with the (independent) calculation in b.) (b) In addition perform a Kuhn-Tucker analysis by writing down the Kuhn-Tucker Lagrangian and the corresponding Kuhn-Tucker equalities and inequalities. Make a comparison with the results derived under (a)