A table is assembled using three components, as shown in the following product structure tree. The company that makes the table wants to ship $230$ units at the beginning of day $4,300$ units at the beginning of day $5,$ and $370$ units at the beginning of day $7.$ Receipts of $230$ wood sections are scheduled at the beginning of day $2.$ There are $270$ legs on hand. An additional $10$ percent of the order size on legs is added for scrap allowance. There are $55$ braces on hand. Lead time $($in days$)$ for all items is a function of each order quantity and is shown below.

Order Quantity Lead Time $($days$)$

$13701$

$3719502$

$9511,7003$

Production Schedule

Day Beg. Inv. $1234567$

Quantity $230300370$