Solve the dual of the following linear programming problem using the simplex method. 𝑀𝑎𝑥𝑖𝑚𝑖𝑧𝑒 𝑃 = 20𝑥 + 30𝑦 + 45𝑧 𝑠𝑢𝑏𝑗𝑒𝑐𝑡 𝑡𝑜 20𝑥 + 40𝑦 + 30𝑧 ≤ 800 30𝑥 + 20𝑦 + 40𝑧 ≤ 800 20𝑥 + 10𝑦 + 30𝑧 ≤ 1000 𝑥 ≥ 0, 𝑦 ≥ 0, 𝑧 ≥ 0
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