I need help with one Finite Math problem.  I need it done within the next hour

I need to show the work and the correct answer.  Thanks.

Here is the question:

6)  Maximize        z =           3^X_{1   +}      2^x₂

subject to:     ^X_{1   +}^x₂= 5

                        4^X_{1   +}2^x₂   ≥  12

                        5^X_{1   + 2}^x₂   ≤  16

                      ^X_{1≥0   +} x_2≥0        

A) Maximum is 14 for ^X₁=4,  ^X₂=1  

B) Maximum is 12 for ^X₁=2, ^X₂=3  

C) Maximum is 13 for ^X₁=3, ^X₂=2   

D) Maximum is 15 for ^X₁=5, ^X₂=0

The answer is one of the multiple choice above.  But I also need the work shown. It needs to be solved using artifical variables.