a$.$ Complete the following MPS time$-$phased record: $(25$ points$)$

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MPS Lot Size $=x$

The following events occurred during week $1$ :

Actual demand during week $1$ was only $28$ units

The forecast for week $9$ is $6+x$

An order for $4$ in week $2$ was accepted.

An order for $3$ in week $4$ was accepted.

An order for $2$ in week $3$ was accepted.

The MPS in week $1($if any$)$ was produced at the $80\%($round up to the nearest

integer$)$

b$.$ Update the record below after rolling through time.

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MPS Lot Size $=x$