The solution should be similar to what you see below, provided I did not make any mistakes.
Let x be the number of artisans and y the number of apprentices.
0 <= x + y <= 16 (he cannot accommodate more than 16 employees - note that you cannot have -1 employees, hence the greater than or equal to zero )
1/2<y/x<9/2 (ratios of apprentices to artisans).
Now, for the number of units,
0<= 9x + 6y <= 72 (an artisan produces 9 units while an apprentice produces 6)