Find the optimal solution for the following problem.
Minimize C = 4x + 12y + 3z
subject to 15x + 5y + 12z ≥ 75
6x + 2y + 8z ≥ 150
and x ≥ 0, y ≥ 0, z ≥ 0.

What is the optimal value of x?
What is the optimal value of y?
What is the optimal value of z? (Round your answer to 3 decimal places.)
What is the minimum value of the objective function? (Round your answer to 3 decimal places.)

Please show your work