Question: Solve this linear programming (LP) problem using the transportation method. Find the optimal transportation plan and the minimum cost. Also, decide if there is an

Solve this linear programming (LP) problem using the transportation method. Find the optimal transportation plan and the minimum cost. Also, decide if there is an alternate solution. If there is one, identify it.

Minimize

8x11 + 2x12 + 5x13 + 2x21 + x22 + 3x23 + 7x31 + 2x32 + 6x33

Subject to

x11 + x12 + x13 = 90

x21 + x22 + x23 = 105

x31 + x32 + x33 = 105

x11 + x21 + x31 = 75

x12 + x22 + x32 = 75

All variables ≥ 0

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