Find the minimum cost solution for the transportation problem detailed in the table below. COSTS Dest 1 Dest 2 Dest 3 Supply Source 1 18 12 5 20 Source 2 10 14 12 30 Source 3 9 11 15 75 Demand 40 30 55 125 \ 125 \begin{array} { | l r | r | r | r | } \hline ext { COSTS } & ext { Dest 1 } & ext { Dest 2 } & ext { Dest 3 } & ext { Supply } \\hline ext { Source 1 } & 18 & 12 & 5 & 20 \\hline ext { Source 2 } & 10 & 14 & 12 & 30 \\hline ext { Source 3 } & 9 & 11 & 15 & 75 \\hline ext { Demand } & 40 & 30 & 55 & 125 \backslash 125 \\hline\end{array} COSTS Source 1 Source 2 Source 3 Demand Dest 1 18 10 9 40 Dest 2 12 14 11 30 Dest 3 5 12 15 55 Supply 20 30 75 125\125 Before your solution can be implemented, you discover that the combination Source 3 - Destination 1 is unavailable, due to political turmoil in the country where Source 3 is located. Solve the revised problem. How much is cost increased by this complication?

Question

Find the minimum cost solution for the transportation problem detailed in the table below.    COSTS   Dest 1   Dest 2   Dest 3   Supply   Source 1  18 12 5 20  Source 2  10 14 12 30  Source 3  9 11 15 75  Demand  40 30 55 125 \ 125 \begin{array} { | l r | r | r | r | } \hline 	ext { COSTS }  &  	ext { Dest 1 }  &  	ext { Dest 2 }  &  	ext { Dest 3 }  &  	ext { Supply } \\hline 	ext { Source 1 }  &  18  &  12  &  5  &  20 \\hline 	ext { Source 2 }  &  10  &  14  &  12  &  30 \\hline 	ext { Source 3 }  &  9  &  11  &  15  &  75 \\hline 	ext { Demand }  &  40  &  30  &  55  &  125 \backslash 125 \\hline\end{array}  COSTS   Source 1   Source 2   Source 3   Demand  ​  Dest 1  18 10 9 40 ​  Dest 2  12 14 11 30 ​  Dest 3  5 12 15 55 ​  Supply  20 30 75 125\125 ​ ​   Before your solution can be implemented, you discover that the combination Source 3 - Destination 1 is unavailable, due to political turmoil in the country where Source 3 is located. Solve the revised problem. How much is cost increased by this complication?

Ronil Bonnet · Accepted Answer

Final Answer :  The first solution is in the first table; cost of this solution is $1,225.    COSTS   Dest. 1   Dest. 2   Dest. 3   Supply   Source 1  20 20  Source 2  30 30  Source 3  40 30 55 75  Demand  40 30 55 125 / 125 \begin{array} { | l | r | r | r | r | } \hline 	ext { COSTS }  &  { 	ext { Dest. 1 } }  &   { 	ext { Dest. 2 } }  &  	ext { Dest. 3 }  &  	ext { Supply } \\hline 	ext { Source 1 }  &   &   &  20  &  20 \\hline 	ext { Source 2 }  &   &   &  30  &  30 \\hline 	ext { Source 3 }  &  40  &  30  &  55  &  75\\hline 	ext { Demand }   &  40  &  30  & 55 &  125/125 \\hline\end{array}  COSTS   Source 1   Source 2   Source 3   Demand  ​  Dest. 1  40 40 ​  Dest. 2  30 30 ​  Dest. 3  20 30 55 55 ​  Supply  20 30 75 125/125 ​ ​   The revision is accomplished by assigning the prohibited cell a very high cost, such as $1,000. This solution appears in the second table; its cost is $1,535. The increase in cost is $310.    COSTS   Dest. 1   Dest. 2   Dest. 3   Supply   Source 1  10 10 20  Source 2  30 30  Source 3  30 45 75  Demand  40 30 55 125 \ 125 \begin{array} { | l | r | r | r | r | } \hline 	ext { COSTS }  &  	ext { Dest. 1 }  &  { 	ext { Dest. 2 } }  &  	ext { Dest. 3 }  &  	ext { Supply } \\hline 	ext { Source 1 }  &  10  &   &  10  &  20 \\hline 	ext { Source 2 }  &  30  &   &   &  30 \\hline 	ext { Source 3 }  &   &  30  &  45  &  75 \\hline	ext { Demand }  &  40  &  30  &  55  &  125 \backslash 125 \\hline\end{array}  COSTS   Source 1   Source 2   Source 3   Demand  ​  Dest. 1  10 30 40 ​  Dest. 2  30 30 ​  Dest. 3  10 45 55 ​  Supply  20 30 75 125\125 ​ ​

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