Due to an existential crisis, the manager at Dan's Danimal Palace is worried about their strategy to buy their cages from a manufacturer, rather than make it themselves. Determine the amount of demand for cages that the manager at Dan's Danimal Palace would be indifferent to buying or making the cages $($hint: the breakeven quantity$).$ Relevant metrics are below.

$\backslash$table$[[\backslash$table$[[$Fixed cost to$],[$buy the cages$],[($e$.$g$.,$ fleet of$],[$trucks and the$],[$warehouse$)]],\backslash$table$[[$Fixed cost$],[$to make the$],[$cages $($e$.$g$.,],[$machinery$)]],\backslash$table$[[$Per unit cost$],[$to buy the$],[$cages$]],\backslash$table$[[$Per unit cost$],[$to make the$],[$cages$]]],[$$$12,881,$$$49,689,\backslash$table$[[$$$16\mathrm{.}50$ per$],[$cage$]],\backslash$table$[[$$$9\mathrm{.}51$ per$],[$cage$]]]]$

Round your answer to the nearest unit of demand $($e$.$g$.,167\mathrm{.}85$ would be $168).$