A manufacturing site would like to determine optimal operating levels for their electric generators and associated distribution patterns that will satisfy the site user demand. Consider the following proposed system.

Generators

Demand

Site

$8$ kWh

$1$

$1$

$4$ kWh

$2$

$7$ kWh

$10$ kWh

$2$

$3$

$6$ kWh

The distribution costs are:

Cost, $($$$/$kWh$)$

Site $1$

Site $3$

SUPPLY $($kWh$)$

Generator $1$

$10$

$15$

$18$

$8$

Generator $2$

$8$

$12$

$13$

$10$

DEMAND $($kWh$)$

$4$

Site $2$

$7$

$6$

Formulate an LP problem and determine the optimal power distribution.