Nino Spirelli has constructed the following $($partial$)$ time$-$phased MPS record:Power Tools $($PT$)$ has just received an order for $70PT$ band saws, to be shipped at the beginning of week $9.$ Information concerning the saw assembly is given here:

$\backslash$table$[[$PT Band Saw$],[$Item$,$Lead Time $($weeks$),$Components$],[$Saw$,2,A(2^{**}),B,C(3)$

$\backslash$table$[[,\backslash$table$[[$On$],[$hand$]],$Week$],[,1,2,3,4,5,6],[$Forecast$,20,30,20,30,20,30],[$Orders$,14,8,6,,,],[\backslash$table$[[$Projected available$],[$balance$]],5,,,,,,],[$Available$-$to$-$promise,,,,,,$],[$MPS$,50,,50,,50,50]]$

a$.$ Complete the record.

b$.$ Are there any problems?

c$.$ What's the earliest Nino can promise an order for $44$ units?

d$.$ Assume that an order for $15$ is booked for week $4.$ Assume the order for $44$ units in part $c$ is not booked; recompute the record.