For the transportation problem below, construct an initial feasible solution using the intuitive method. COSTS Dest. 1 Dest. 2 Dest. 3 Dest. 4 Supply Source 1 12 18 9 11 45 Source 2 19 7 30 15 145 Source 3 8 10 14 16 50 demand 80 30 70 60 240 1240 \begin{array} { | l r | r | r | r | r | } \hline ext { COSTS } & { ext { Dest. 1 } } & ext { Dest. 2 } & ext { Dest. 3 } & ext { Dest. 4 } & ext { Supply } \\hline ext { Source 1 } & 12 & 18 & 9 & 11 & 45 \\hline ext { Source 2 } & 19 & 7 & 30 & 15 & 145 \\hline ext { Source 3 } & 8 & 10 & 14 & 16 & 50 \\hline ext { demand } & 80 & 30 & 70 & 60 & 240 ext { 1240 } \\hline\end{array} COSTS Source 1 Source 2 Source 3 demand Dest. 1 12 19 8 80 Dest. 2 18 7 10 30 Dest. 3 9 30 14 70 Dest. 4 11 15 16 60 Supply 45 145 50 240 1240

Question

For the transportation problem below, construct an initial feasible solution using the intuitive method.    COSTS   Dest. 1   Dest. 2   Dest. 3   Dest. 4   Supply   Source 1  12 18 9 11 45  Source 2  19 7 30 15 145  Source 3  8 10 14 16 50  demand  80 30 70 60 240  1240  \begin{array} { | l r | r | r | r | r | } \hline 	ext { COSTS }  &   { 	ext { Dest. 1 } }  &  	ext { Dest. 2 }  &  	ext { Dest. 3 }  &  	ext { Dest. 4 }  &  	ext { Supply } \\hline 	ext { Source 1 }  &  12  &  18  &  9  &  11  &  45 \\hline 	ext { Source 2 }  &  19  &  7  &  30  &  15  &  145 \\hline 	ext { Source 3 }  &  8  &  10  &  14  &  16  &  50 \\hline 	ext { demand }  &  80  &  30  &  70  &  60  &  240 	ext { 1240 } \\hline\end{array}  COSTS   Source 1   Source 2   Source 3   demand  ​  Dest. 1  12 19 8 80 ​  Dest. 2  18 7 10 30 ​  Dest. 3  9 30 14 70 ​  Dest. 4  11 15 16 60 ​  Supply  45 145 50 240  1240  ​ ​

Sherise Nutzmann · Accepted Answer

Final Answer :  The lowest cost in the matrix is 7; assign 30 units to S2D2 and rule out all other cells in D2. Now the lowest cost in the table is 8; assign 50 units to S3D1 and rule out all other cells in S3. The smallest cost is now 9; assign 45 units to S1D3 and rule out all other S1. The remaining assignments are 60 units to S2D4, 30 units to S2D1, and 25 units to S2D3. These assignments are summarized in the table below.    Intuitive   Dest. 1   Dest. 2   Dest. 3   Dest. 4   Supply   Source 1  45 45  Source 2  30 30 25 60 145  Source 3  50 50  Demand  80 30 70 60 240 / 240 \begin{array} { | l | r | r | r | r | r | } \hline 	ext { Intuitive }  &   { 	ext { Dest. 1 } }  &  { 	ext { Dest. 2 } }  &  	ext { Dest. 3 }  &  { 	ext { Dest. 4 } }  &  	ext { Supply } \\hline 	ext { Source 1 }  &   &   &  45  &   &  45 \\hline 	ext { Source 2 }  &  30  &  30  &  25  &  60  &  145 \\hline 	ext { Source 3 }  &  50  &   &   &   &  50 \\hline  	ext { Demand }  &  80  &  30  &  70  &  60  &  240/240\\hline\end{array}  Intuitive   Source 1   Source 2   Source 3   Demand  ​  Dest. 1  30 50 80 ​  Dest. 2  30 30 ​  Dest. 3  45 25 70 ​  Dest. 4  60 60 ​  Supply  45 145 50 240/240 ​ ​

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