Manaal! there's a really cool method that does not require a calculator. the goal into meet demand and still fit the supply limits. We called it NW corner method. You need excel to determine the cost but here is how it works:
1) start on the top left hand corner.
2) find the smallest cost across the first row: 500.
3) use tuscon's supply to meet Charleston's demand: 25.
4) draw a line through Tuscon and Charleston: horizontal and vertical.
5) find the next open NW corner and fin the lowest in the available row: 650 with Seattle meeting nashville's demands.
6) use seattle's supply to meet nashville's demands:25.
7) cross out Seattle as a supply port with horizontal line. Then cross out the demand of 40 for Nashville, subtract 25, and write in 15. 15 left for Nashville!
8) find the next NW corner and find te lowest in the available row: 550 using baltimore's supply to meet nashville's demand.
9) use baltimore's supply to fill nashville's demand: 10.
10) cross out Baltimore as a supply port with a horizontal line. Cross out the remaining demand for Nashville, subtract ten, an write in five left for demand.
11) find the next open NW corner left and identify the lowest cost:620.
12) use detroit's supply to meet the remaining five of nashville's needs.
13) cross out Nashville as a demand with a vertical line.
14) cross out the supply at Detroit, subtract 5, write in 20.
15) find the next NW corner: 905 with Miami as open demand unmet.
16) use detroit's last 20 units to meet miami's demand.
So that means 25*500+650*25+10*550+5*620+20*905 is the minimized cost. There's variations of this called vogel's cost that may net something lower. So let me know if you're interested in that too.