Final answer:
The given problem involves solving for z with the given constraints using linear equations and inequalities.
Step-by-step explanation:
The given problem involves solving for z with the given constraints using linear equations and inequalities.
We have the equation z = 18x + 30y, and the constraints 3x + 3y > 9, -x + 4y < 12, and 4x - y < 12.
We can solve this problem by graphically determining the feasible region of the constraints and evaluating the equation z = 18x + 30y at the boundary points of the region to find the maximum value of z.