ABC bank is open from $09\mathrm{.}00$ to $17\mathrm{.}00$ from Monday to Friday. Based on past experience, it requires the number of elements given in the table below.

Time Range Required Employee

$09\mathrm{.}00-10\mathrm{.}004$

$10\mathrm{.}00-11\mathrm{.}003$

$11\mathrm{.}00-12\mathrm{.}004$

$12\mathrm{.}00-13\mathrm{.}006$

$13\mathrm{.}00-14\mathrm{.}005$

$14\mathrm{.}00-15\mathrm{.}006$

$15\mathrm{.}00-16\mathrm{.}008$

$16\mathrm{.}00-17\mathrm{.}008$

The bank employs two types of employees. Full$-$time employees work $5$ days a week between $09\mathrm{.}00-17\mathrm{.}00,$ excluding a one$-$hour lunch break $($The bank determines when the full$-$time employee goes to lunch. However, each employee must go either between $12\mathrm{.}00-13\mathrm{.}00$ or between $13\mathrm{.}00-14\mathrm{.}00).$ Full$-$time employees are paid $$8$ per hour $($including meal hours$).$ The bank also hires part$-$time staff. Each part$-$time employee must work $3$ consecutive hours per day. Part$-$time employees receive $$5$ per hour. The bank has decided that a maximum of five part$-$time employees can be employed in order to provide adequate service quality. Build a mathematical model that meets employee needs at minimum cost.