Brittney wants to develop the inventory record for Item B using the lot$-$for$-$lot $($L$4$L$)$ rule. Item $B$ is one of the components necessary for producing Product $A.$ The bill of material $($BOM$)$ shows that two units of the component are needed to produce one unit of the product. The order quantity is based on the L$4$L lot$-$sizing rule. The lead time is $1$ week. The current on$-$hand inventory, also called the beginning inventory, is $20$ units. The company has the scheduled receipt of $10$ units in Week $1.$ The MPS start quantities of the product for the next $4$ weeks are shown in the table below. Round to the nearest whole number.

$[$Note: Projected on$-$hand inventory balance at the end of week $t=$ Inventory on hand at the end of week $t-1+$ Scheduled or planned receipts in week $t-$ Gross requirements in week $t.$ POQ lot size in week $t=$ Total gross requirements for $P$ week, including week $t-$ Projected on$-$hand inventory balance at the end of week $t-1.$

L$4$L lot size in week $t=$ Gross requirements for week $t-$ Projected on$-$hand inventory balance at the end of week $t-1.]$

Table $1.$ MPS Start Quantity for Product A

$\backslash$table$[[$Product: A$,1,2,3,4],[$MPS Start,$6,11,3,13$

QUESTION:

What is the gross requirement for item $"$B$"$ in week $2?$

What is the planned receipt for item B in week $4$ and week $1?$

What is the projected on hand inventory for B in week $4$ and week $1?$