Tabard Industries forecasted the following demand

for one of its most profitable products for the next $8$ weeks: $120,120,120,100,100,100,80,$ and $80$ units. The booked customer orders for this product, starting in week $1,$ are $100,80,60,40,10,10,0,$ and $0$ units. The current on$-$hand inventory is $150$ units, the order quan$-$ tity is $200$ units, and the lead time is $1$ week.

a$.$ Develop an MPS for this product.

b$.$ The marketing department revised its forecast. Starting with week $1,$ the new forecasts are $120,120,120,150,150,150,100,$ and $100$ units. Assuming that the prospective MPS you developed in part

$($a$)$ does not change, prepare a revised MPS record. Comment on the situation that Tabard now faces.

c$.$ Returning to the original forecasted demand level and the MPS record you developed in part $($a$),$ assume that marketing accepted a new customer order for $200$ units in week $2,$ and thereby booked orders in week $2$ now total $280$ units. Assuming that the prospective MPS you developed in part $($a$)$ does not change, prepare a revised MPS record. Comment on the situation that Tabard now faces.