Find the maximum and minimum values of the function f(x,y)=exy\displaystyle {f{{\left({x},{y}\right)}}}={e}^{{{x}{y}}} subject to x3+y3=128\displaystyle {x}^{{3}}+{y}^{{3}}={128}

Maximum value:  
Minimum value:  

Enter DNE if the value does not exist.