$,,$Marie Bain is the production manager at a company that manufactures hot water heaters.

Marie needs a demand forecast for the next few years to help decide whether to add new

production capacity. The company's sales history $($in thousands of units$)$ is shown in the

table below. Use exponential smoothing with trend adjustment to forecast demand for

period $3.$ The initial forecast for period $1$ was $10$ units; the initial estimate of trend was $1\mathrm{.}5.$

The smoothing constants are $=\mathrm{.}5$ and $=\mathrm{.}4$

Period Actual

$1,12$

$2,15$

$3,16$

$4,16$

$5,18$

$620$

$17\mathrm{.}48$

$12\mathrm{.}89$

$16\mathrm{.}11$

$19\mathrm{.}67$