$16\mathrm{.}17$ A manufacturer of television sets has three factories, located in Philadelphia, St$.$ Louis, and Phoenix. The company has four distribution centers, located in Atlanta, Chicago, Denver, and Seattle. All of the products are shipped from a factory to a distribution center, from which they are distributed to various customers across the country.

The plant capacities and distribution requirements $($demands$),$ in units per month, and shipping costs, in dollars per unit, are given below.

$\backslash$table$[[$Philadelphia$,$St$.$ Louis,Phoenix$],[5,000,8,000,12,000]]$

$\backslash$table$[[$Atlanta$,$Chicago,Denver,Seattle$],[6,000,8,000,5,000,6,000]]$

$\backslash$table$[[$From: $,$Philadelphia,St$.$ Louis,Phoenix$],[$To: Atlanta,$$100,$$$125,$$$300$