Suppose that you have:

Factories F$\_1,$ F$\_2,$ and F$\_3$

Transshipment points W$\_1,$ W$\_2,$ and W$\_3$

Destinations D$\_1,$ D$\_2,$ D$\_3,$ and D$\_4$

The costs for shipping are shown in the Excel spreadsheet below. $($Notice that $$999$ is a very high cost $$ for example, there is no shipping route between F$\_1$ and D$\_1.)$

The decision variables are found in a corresponding portion of the sheet, C$9$:I$14.$

What is the objective function?

Shipping costs

$->$ W$1$ W$2$ W$3$ D$1$ D$2$ D$3$ D$4$

F$14\mathrm{.}686\mathrm{.}819\mathrm{.}31999999999999$

F$25\mathrm{.}036\mathrm{.}6710\mathrm{.}04999999999999$

F$36\mathrm{.}854\mathrm{.}678\mathrm{.}75999999999999$

W$19999999999\mathrm{.}0911\mathrm{.}864\mathrm{.}069\mathrm{.}61$

W$29999999996\mathrm{.}113\mathrm{.}7210\mathrm{.}811\mathrm{.}08$

W$39999999992\mathrm{.}583\mathrm{.}432\mathrm{.}63\mathrm{.}79$

$=$SUMPRODUCT $($C$9$:I$14)*$ SUMPRODUCT $($C$2$:I$7)$

$=$SUMPRODUCT$($C$9$:I$14,$ C$2$:I$7)$

$=$SUMPRODUCT$($C$2$:E$7,$ F$2$:I$7)$

$=$SUMPRODUCT$($C$2$:I$7,$ J$2$:P$7)$