The following table contains the demand for the last $10$ months:

$\backslash$table$[[$Month$,$Actial Demand$],[1,31],[2,34],[3,33],[4,35],[5,37],[6,36],[7,35],[8,40],[9,45],[10,41]]$

a$)$ Calculate the single exponential smoothing forecast for these data using apha $=0\mathrm{.}30$ and an initial forecast of $31.[4$M$]$

b$)$ Calculate the exponential smoothing with trend forecast for these data using an alpha of $0\mathrm{.}30$ and beta of $0\mathrm{.}30,$ an initial trend forecast of $1$ and an in itial smocthed forecast of $30.$

$[4$M$]$