c$.$ In considering the most desirable capital structure of a company the following data have been collected by the finance manager of the company from the capital market:

$\backslash$table$[[\{$

$\backslash$table$[[$Debt as $\%$ of$],[$total capital$]]\},\backslash$table$[[$Cost of debt$],[($In $\%)]],\backslash$table$[[$Cost of equity$],[($In $\%)]]],[5\mathrm{.}0,12\mathrm{.}0],[|)/(|0|),10,5\mathrm{.}0,12],[20,5\mathrm{.}0,12\mathrm{.}5],[30,5\mathrm{.}5,13\mathrm{.}0],[,40,6\mathrm{.}0,14\mathrm{.}0],[,50,6\mathrm{.}5,16\mathrm{.}0],[,60,7\mathrm{.}0,20\mathrm{.}0]]$

You are required to determine the optimal debt$-$equity mix for the company by compu the composite cost of capital. Please give a proper mathematical solution step by step without using excel