1. (i) Consider the following function of two choice variables

Z = f (x,y)

Write down the first order and the second order conditions for a minimum.

(ii) Suppose an individuals health status Z (measured on a scale of 0 to 10) is a function of two health enhancing drugs x and y (measured as daily dosages) as follows.

Z = - x² + 2x - y² + 4y+ 5

1. Find f_x, f_y, f_xy, f_yx, f_xx, f_yy
2. Show that the function has only one stationary point at x = 1 and y = 2 and it is a maximum.

Estimate the value of the health status Z at the point derived at (b