I. The production processes for three goods, C$1,$ C$2,$ C$3$ are interlinked. To produce one dollar's worth of C$1$ requires the input of $$0\mathrm{.}2$ worth of C$1,$ $$0\mathrm{.}4$ of C$2$ and $$0\mathrm{.}1$ of C$3.$ To produce one dollar's worth of C$2$ requires $$0\mathrm{.}3$ worth of C$1,$ $$0\mathrm{.}1$ worth of C$2$ and $$0\mathrm{.}3$ worth of C$3,$ and to produce one dollar's worth of C$3$ requires $$0\mathrm{.}2$ worth of each of Cl$,$ C$2$ and C$3.$ Suppose that, in a given time period, there is an external demand for d$1$ dollars' worth of CI$,$ d$2$ of C$2$ and d$3$ of C$3.$ What are the production levels Xl$,$ X$2,$ X$3$ of C$1,$ C$2,$ C$3$ required to satisfy all demands in the given period?