$($VECTOR SPACE$)$ An engineering project involving the construction of a renewable energy plant. There are

three main sectors involved in the construction process: the production of solar panel,

the manufacturing of energy storage systems, and the construction of supporting

infrastructure.

It takes $0\mathrm{.}02$ units of solar panels, $0\mathrm{.}06$ units of energy storage systems, and $0\mathrm{.}10$ units

of infrastructure to produce $1$ unit of solar panels.

It takes $0\mathrm{.}40$ units of energy storage systems and $0\mathrm{.}04$ units of infrastructure to produce

$1$ unit of energy storage systems.

It takes $0\mathrm{.}18$ units of solar panels, $0\mathrm{.}01$ units of energy storage systems, and $0\mathrm{.}10$ units

of infrastructure to construct $1$ unit of infrastructure.

What should the total production be set at in order to satisfy an external demand of $200$

units of solar panel, $180$ units of energy storage systems and $175$ units of infrastructure?