(a) Suppose the following: is function of Q1, Q2 and Q3: = 4Q 2^1 11Q2 + Q2Q3 + Q1Q3 + Q 2^2 + Q 2^3

i) (3 points) Write down the first order conditions.

ii) (20 points) Rewrite (i) in its matrix form and find the stationary point (Q1, Q2, Q3). Find the optimum USING ALL of the following methods: Gaussian elimination, Cramer's rule and inverse matrix.

iii) (7 points) Use Hessian Matrix and its leading principle minors to determine if this optimum is at maximum or minimum or neither.

(b) (8 points) Find the extreme value and determine if at the point the function is at maximum, minimum or neither.

i) f(x, y, z) = x^2 + 3y^2 3xy + 4yz + 6z^2