Consider an economy with three sectors: mining, electricity, and robotics. Mining sells $30\%$ of it output to electricity, $50\%$ to robotics, and retains the rest. Electricity sells $80\%$ of its output t mining, $10\%$ to robotics, and retains the rest. Robotics sells $40\%$ to mining, $40\%$ to electricity, an retains the rest.

Find a set of equilibrium prices $($that is$,$ prices at which each sector$\text{'}$s income matches its expenses when the price for the robotics output is $$100$ million.