A table is assembled using three components, as shown in the following product structure tree. The company that makes the table wants to ship $70$ units at the beginning of day $4,110$ units at the beginning of day $5,$ and $150$ units at the beginning of day $7.$ Receipts of $70$ wood sections are scheduled at the beginning of day $2.$ There are $100$ legs on hand. An additional $10$ percent of the order size on legs is added for scrap allowance. There are $40$ braces on hand. Lead time $($in days$)$ for all items is a function of each order quantity and is shown below.