Joeblog imports spectrometers for forensic laboratories and educational institutions. The item$$s demand fore$-$ casts for the next $6$ weeks are $25$ units, followed by fore$-$ casts of $20$ units for weeks $7$ through $10.$ The current

on$-$hand inventory is $50$ units. The order policy is to produce in lots of $75.$ The booked customer orders for the item, starting with week $1,$ are $17,25,10,11,5,10,$ and $5$ units. The lead time is $3$ weeks.

a$.$ Develop an MPS for the spectrometer.

b$.$ The marketing department has received further

orders for this item in the following sequence: Order $1$ is for $35$ units to be delivered in period $4.$ Order $2$ is for $55$ units to be delivered in period $5.$ Order $3$ is for $65$ units to be delivered in period $6.$ Order $4$ is for $35$ units to be delivered in period $7.$ Order $5$ is for $20$ units to be delivered in period $6.$ Order $6$ is for $15$ 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$)?$