The MRP gross requirements for product A in the next $10$ weeks are shown in the following table. The lead time for A is three weeks, and the setup cost is $$300.$ The carrying cost is $$2$ per unit per week. Suppose the initial inventory at the beginning of week $1$ is $150$ units. $(1)$ Determine for what quantity the order should be planned to be received for each week using the following three lot$-$sizing methods: lot$-$for$-$lot, least total costs, and least unit cost. $($Hint: start from the week when the initial inventory is insufficient to satisfy the gross requirements$).$