Consider the following problem, where the value of k has not yet been ascertained.

Maximize Z x1  2x2, subject to

x1  x2  2 x2  3 kx1  x2  2k  3, where k  0 and x1  0, x2  0.

The solution currently being used is x1 2, x2 3. Use graphical analysis to determine the values of k such that this solution actually is optimal.