Templeton Engineering has an inventory turnover rate of $10\mathrm{.}60,$ an accounts payable period of $50$ days, and an accounts receivable period of $45$ days. What is the length, in days, of the cash cycle?

$14\mathrm{.}11$

$17\mathrm{.}94$

$21\mathrm{.}77$

$25\mathrm{.}60$

$29\mathrm{.}43$