Given the forecast and booked orders shown in the table, and a beginning inventory of $120,$ what is the MPS for period $4?$ The company operates with a lot size of $144.$

Period

$1$

$2$

$3$

$4$

Forecasted Demand

$500$

$450$

$400$

$600$

Booked Orders

$520$

$400$

$325$

$450$

Projected ending inventory

Master production schedule

Available to Promise

Multiple Choice

$144$

$432$

$576$