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 = ?