Powerhouse produces capacitors at three locations:

Los Angeles, Chicago, and New York. Capacitors

are shipped from these locations to public utilities in

five regions of the country: northeast $($NE$),$ northwest

$($NW$),$ midwest $($MW$),$ southeast $($SE$),$ and southwest

$($SW$).$ The cost of producing and shipping a capacitor

from each plant to each region of the country

is given in the file P$05\_63.$xlsx$.$ Each plant has an