Given the following demand data,

Period Demand

$157$

$255$

$359$

$456$

$560$

a$.$ Compute a weighted average forecast using a weight of $0\mathrm{.}4$ for the most recent period, $0\mathrm{.}3$ for the next most recent, $0\mathrm{.}2$ for the next, and $0\mathrm{.}1$ for the next. $($Round all your answers to two decimal points.$)$

b$.$ If the actual demand for period $6$ is $58,$ forecast demand for period $7$ using the same weights as in part a$.$