The Wheat Shipping Example

Shipping costs $($$$/$ton$)$

$\backslash$table$[[,$Mills,,Grain$],[$Grain Elevators,A Chicago,B St$.$ Louis,C Cincinnati,Supply,Shipped$],[1$ Kansas City,,,,$150,],[2$ Omaha,,,,$175,],[3,,,,275,],[$Demand$,200,100,300,600,],[$Grain Shipped,,,,,$],[$Cost $=,,,,,]]$

$\backslash$table$[[,$Mills$],[$Grain Elevators,Chicago,St$.$ Louis,Cincinnati$],[$Kansas City,$6,8,10],[$Omaha$,7,11,11],[$Des Moines,$4,5,12]]$

minimize $Z=6x_{1A}+8x_{1B}+10x_{1C}+7x_{2A}+11x_{2B}+11x_{2C}+4x_{3A}+5x_{3B}+12x_{3C}$ subject to

$x_{1A}+x_{1B}+x_{1C}=150$

$x_{2A}+x_{2B}+x_{2C}=175$

$x_{3A}+x_{3B}+x_{3C}=275$

$x_{1A}+x_{2A}+x_{3A}=200$

$x_{1B}+x_{2B}+x_{3B}=100$

$x_{1C}+x_{2C}+x_{3C}=300$

$x_{ij}0$