$1)$ Following table shows forecast and orders received for a specific product for eight months. Beginning inventory for this product is $50$ units and there are scheduled receipts of $200$ units in month $4.$

a$.$ Calculate net requirements.

b$.$ Calculate the MPS if the product is produced in lots of $400$ units $($use lead time of $0)$ and projected$-$on$-$hand inventory by period for the master schedule.

c$.$ Because of union regulations, capacity for month $3$ and $4$ will be decreased to $400$ labor hour from $800$ labor hour. Since, each unit of product requires $2$ labor hours to produce, revise MPS according to capacity requirements.

d$.$ Calculate the available$-$to$-$promise $($ATP$)$ using the discrete $($period$-$by$-$period$)$ method.

e$.$ Calculate the available$-$to$-$promise $($ATP$)$ using the cumulative with look$-$ahead method.

f$.$ Calculate the projected$-$on$-$hand $\backslash ((\backslash$mathrm$\{$POH$\})\backslash )$ using the consuming forecast method and the assumption that orders are following their normal pattern $($the original forecast is still valid$).$

g$.$ Calculate the projected$-$on$-$hand using the consuming forecast method and the assumption that $100$ units are ordered in Month $6$ are from a new customer. All other orders are following their normal pattern $($the original total forecast must be increased$).$

h$.$ Using the receipt of an additional order for $50$ units in Month $7,$ calculate both the ATP $($with look ahead$)$ and the revised POH.