The temperature in the steam room of the Star Ship Enterprise is given by the following function:

$\displaystyle T(x,y) = 100 - 4x^{2} -y^{2} + x^{2}y^{2}-1 $

$\displaystyle -1 \leq x \leq 1 $

$\displaystyle -2 \leq y \leq 3 $

Captain Kirk likes the hottest temperature while Mr Spock prefers the coolest area of the steam room.

Where should each of them sit? Why?