Question

The costs of mining and transporting coal are roughly independent of the heating value of the coal. Consider that the coal in the ground is valued at 50 cents/(million kJ), that mining costs are 8 dollars/(short-ton), and that transportation costs are 8 cents/(short-tonꞏmile). If the price of other delivered coals is 160 cents/(million kJ), find: (a) the radius from the mine, in miles, that a coal of 32,560 kJ/kg can be delivered and sold for zero profit or loss; (b) the same radius for a coal with a heating value of 23,200 kJ/kg; and (c) the minimum heating value of a coal that could be used locally (i.e., a mine mouth plant).

Answer 1

Loal in peurd Pitg lest = kn tan foYMh on les eents/hom-dle pire delivend by oa bo ents 92510 lue loa 32160 Heatg Value (oal So, iuired oal З2/60 4 юоина 0.0163/y 30.71 alate minn (ost Me .0.009/t MC 000

trand Pos hhon chasyi akdakh 0.09 looo Dehvered Ceal fost 1bo cent $1.60 mlion 30. 71 Consider Dese Vay coal paice mived loal los $0.008+$0.0000x) $0.0163 .052 Ba.003 0 00 2 77 3H625 miley

2 3200 k7lg lo00o00 23200 $0.5 3.10 - H3.1o

Aels Assume MIntd Coal Cos Delivery tod togh a ol 6$0.008+o. 0000P$a037 2 17.5 Miley minimyw (o S Value -Valve frount +roln Hy is heahg alUe atmine moune 160 tens мt 67 k /,0.5t0003% Hv Vale at mine mout