A certain economy has three interdependent sectors: oil, electricity, and grain. To produce $$1$ of oil requires $$0\mathrm{.}1$ of oil, $$0\mathrm{.}15$ of electricity, and

$$0\mathrm{.}7$ of grain. To produce $$1$ of electricity requires $$0\mathrm{.}25$ of oil, $$0\mathrm{.}55$ of electricity, and $$0\mathrm{.}15$ of grain. To produce $$1$ of grain requires $$0\mathrm{.}35$ of

oil, $$0\mathrm{.}2$ of electricity, and $$0\mathrm{.}35$ of grain.There is also an external demand for $$15000$ of oil, $$15000$ of electricity, and $$2000$ of grain.

To meet the external demand, the economy must produce $ of oil, $ of electricity, and $ of grain.

Under this production schedule, the internal consumption of the economy is $ of oil, $ of electricity, and $ of grain.

Note: for this problem, You can do your matrix calculations on a computer! MIO for details if you are having difficulties.