Solve this linear programming problem using the simplex method:

Maximize P = 21x + 12y + 24z subject to these constraints:

3x + 2y + 3z ≤ 864
15x + 6z ≤ 1296
9x + 8y + 18z ≤ 4608
x ≥ 0, y ≥ 0, z ≥ 0

Maximum value for P = ?.

This value of P occurs when:
x = ?
y = ?
z = ?

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