5. There is a LP model: (48 points) max z = 7x + 2x +10x3 x...

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5. There is a LP model: (48 points) max z = 7x₁ + 2x₂ +10x3 x₁ + 2x₂ + 3x₂ ≤300 3x₁ + 2x₂ + 3x3 ≤ 600 (X₁₂ X ₂₂ X3 ≥ 0 (1) What are the optimal solution and value of objective function? (14') ¶ (2) Write the optimal solution of dual problem according to the final table. (5¹) 1 (3) Please write the following vectors and matrices according to the model and final table. (5') N, B-¹P59 B-¹b, CB, P₁1 (4) Verify that the final table is correct; (5¹) ¶ (5) What's the allowable range of c3 that enable the optimal base to remain unchanged? (7) 1 (6) If b₁' =800, does the optimal basic matrix change? If changes, what are the new optimal solution and the value of objective function? (12') ¶ 5. There is a LP model: (48 points) max z = 7x₁ + 2x₂ +10x3 x₁ + 2x₂ + 3x₂ ≤300 3x₁ + 2x₂ + 3x3 ≤ 600 (X₁₂ X ₂₂ X3 ≥ 0 (1) What are the optimal solution and value of objective function? (14') ¶ (2) Write the optimal solution of dual problem according to the final table. (5¹) 1 (3) Please write the following vectors and matrices according to the model and final table. (5') N, B-¹P59 B-¹b, CB, P₁1 (4) Verify that the final table is correct; (5¹) ¶ (5) What's the allowable range of c3 that enable the optimal base to remain unchanged? (7) 1 (6) If b₁' =800, does the optimal basic matrix change? If changes, what are the new optimal solution and the value of objective function? (12') ¶