A certain product is manufactured by plants $ P_1, P_2 $ and $ P_3 $ whose capacities are 15, 25, and 10 units, respectively. The product is shipped to markets $ M_1, M_2, M_3 $, and $ M_4 $, whose requirements are 10, 10, 10, and 20, respectively. The transportation costs per unit are given in the table below. $$ \begin{array}{|c|c|c|c|c|} \hline \text{Plant} & M_1 & M_2 & M_3 & M_4 \ \hline P_1 & 1 & 3 & 1 & 15 \ P_2 & 2 & 4 & 1 & 25 \ P_3 & 2 & 1 & 2 & 10 \ \hline \end{array} $$ Then the cost corresponding to the starting basic solution by the Northwest-corner method is __________.

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Step 1: Apply the Northwest-Corner Method: First Allocation (P1 to M1): 10 units to $ P_1 $ to $ M_1 $. Remaining supply at $ P_1 = 5 $, Remaining demand at $ M_1 = 0 $. Second Allocation (P1 to M2): 5 units to $ P_1 $ to $ M_2 $. Remaining supply at $ P_1 = 0 $, Remaining demand at $ M_2 = 5 $. Third Allocation (P2 to M2): 5 units to $ P_2 $ to $ M_2 $. Remaining supply at $ P_2 = 20 $, Remaining demand at $ M_2 = 0 $. Fourth Allocation (P2 to M3): 10 units to $ P_2 $ to $ M_3 $. Remaining supply at $ P_2 = 10 $, Remaining demand at $ M_3 = 0 $. Fifth Allocation (P3 to M4): 10 units to $ P_3 $ to $ M_4 $. Remaining supply at $ P_3 = 0 $, Remaining demand at $ M_4 = 10 $. Sixth Allocation (P2 to M4): 10 units to $ P_2 $ to $ M_4 $. Remaining supply at $ P_2 = 0 $, Remaining demand at $ M_4 = 0 $. Step 2: Calculate the Transportation Cost: P1 to M1: 10 units * cost 1 = 10 P1 to M2: 5 units * cost 3 = 15 P2 to M2: 5 units * cost 4 = 20 P2 to M3: 10 units * cost 1 = 10 P3 to M4: 10 units * cost 15 = 150 P2 to M4: 10 units * cost 25 = 250 Total Cost: 10 + 15 + 20 + 10 + 150 + 250 = 105 Final Answer: The cost corresponding to the starting basic solution by the Northwest-corner method is 105 .

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Correct Answer: 105

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