The answer to part (a) is given as 307 miles!!!!!!!!! There are many incorrect a

Question

The answer to part (a) is given as 307 miles!!!!!!!!!

There are many incorrect answers given to this question. Please do not copy and paste from previously given solution, as it is most likely incorrect.

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/ton, and that transportation costs are 8 cents/ton-mile. 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).

Explanation / Answer

Solution:

Cost of coal in ground, Cb = 50cents/million-KJ = 0.00005cents/KJ

Mining cost, Cm = 8dollars/1ton = 0.8cents/Kg

Transportation cost, Ct = 8cents/1ton-mile = 0.008cents/mile

Selling price, Cs = 160cents/million-KJ - 0.00016cents/KJ

Now,part (a) q=32,560 KJ/Kg need to be delivered without profit or loss

Let radius of mine be 'r' miles

So, as per need Cb*q+Cm+Ct*r=Cs*q

Therefore, r=347.7 miles

part(b) for q=23,200 KJ/Kg, use the same equation from previous part but with current value of q

r=219 miles

part(c) For a mine mouth plant, mine distance or radius can be assumed to be zero i.e. r=0

so, Cb*q+Cm=Cs*q

qmin=Cm/(Cs-Cb)=7,272.72 KJ/Kg

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