A firm has the following production function for producing "z" , using inputs x and y : Z(x,y) = (x^2 + 3a) (y^2 + b)

The firm must minimize its cost given as: T(x,y) = cx + dy, where $c is unit price of x and $d is e unit price of y .

a) Format the Lagrangian for the firm's optimization problem and derive the first order conditions.

b) Provide brief economic interpretation about the elasticity of substitution.