Question

Essex Energy Company has a contract to deliver 400 tons of coal to China. The company has mines in the following regions - Appalachia (WV, KY, and VA), Mississippi (IL and IN), and Midwest (MO, IA, and NE) - and it ships coal via barges and rail to ports in Baltimore, Norfolk, Mobile, and New Orleans, and from these ports to China. The company ships coal from its Appalachian mines to Baltimore and Norfolk exclusively by rail, and it ships from its Mississippi and Midwest regions to Mobile and New Orleans by barge. All other routes use a combination of rail and barge shipping. The shipping costs per ton from each region to each port and the available supply (in tons) from each region are shown in the following table.

TO
From	Baltimore	Norfolk	Mobile	New Orleans	Supply
WV, KY, VA	21	16	32	28	220
IL, IN	26	30	8	10	130
MO, IA, NE	31	24	7	6	90

Determine the coal shipped from each port at the minimum total shipping cost to meet the company's total contract.

Answer 1

Optimal shipping plan is determined by Solver as follows:

EXCEL FORMULAS:

Optimal shipping plan
From\To	=B2	=C2	=D2	=E2	Sent
=A3	0	180	0	0	=SUM(B10:E10)
=A4	0	0	130	0	=SUM(B11:E11)
=A5	0	0	0	90	=SUM(B12:E12)
Received	=SUM(B10:B12)	=SUM(C10:C12)	=SUM(D10:D12)	=SUM(E10:E12)	=SUM(F10:F12)
Total Cost =	=SUMPRODUCT(B10:E12,B3:E5)

Total shipping cost = 4,460