Bakshi $9\mathrm{.}5$: An Integrated Gasification Combined Cycle $($IGCC$)$ plant can convert coal and water to electricity and hydrogen. The carbon dioxide from such a process may be captured by a doublestage solvent such as Selexol. The main inputs to such a system are $5426$ tonnes of Coal and $21,787m^3$ of water to produce $560$ tons of hydrogen, $30\mathrm{.}3MW$ of electricity, $11,253$ tons of pure carbon dioxide, and $1293$ tons of carbon dioxide in flue gas. The cost of hydrogen is $$2110$ per ton, electricity is $$1800$ per MW$,$ pure CO$2$ is $$37$ per ton, and flue gas is zero $[10].$ Allocate water use among the products of this process by the following approaches and discuss the pros and cons of each approach for this allocation problem.:

i$.$ Mass$-$based allocation

ii$.$ Energy$-$based allocation

iii. Monetary$-$based allocation