Minimize P = 5w₁ + 15w₂ subject to
2w₁ + 5w₂ ≥ 10,
2w₁ + 3w₂ ≥ 12,
4w₂ ≥ 8,
w₁, w₂ ≥ 0

Write down the initial simplex tableau of the corresponding dual problem. Use the simplex algorithm and the theorem of duality to determine the minimum value of P in the primal problem.