$"$An end item$$s demand forecasts for the next $6$ weeks are $30$ units, followed by forecasts of $25$ units for weeks $7$ through $10.$ The current on$-$hand inven$-$

tory is $60$ units. The order policy is to produce in lots of $100.$ The booked customer orders for the item, starting with week $1,$ are $22,30,15,11,0,0,9,$

$0,0,$ and $0$ units. The lead time is $2$ weeks.

a$.$ Develop an MPS for this end item.

b$.$ The marketing department has received six orders for this item in the following sequence:

Order $1$ is for $40$ units to be delivered in period $3.$

Order $2$ is for $60$ units to be delivered in period $4.$

Order $3$ is for $70$ units to be delivered in period $6.$

Order $4$ is for $40$ units to be delivered in period $3.$

Order $5$ is for $20$ units to be delivered in period $5.$

Order $6$ is for $115$ units to be delivered in period $9.$

Assuming that the prospective MPS you developed in part $($a$)$ does not change, which orders would you be able to accept based on the available to promise $($ATP$)?"$