$($please calculate by hand no excel$)$

Question $2.$ Material Requirements Planning $(25$ marks$)$

The MRP gross requirements for product A in the next $12$ weeks are shown in the following table. The lead time

for A is two weeks, and the setup cost is $$200.$ The carrying cost is $$0\mathrm{.}3$ per unit per day. Suppose the initial

inventory at the beginning of week $1$ is $130$ units.

Questions:

$(1)$ 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: production should be scheduled

when the initial inventory are all consumed. $(3$ marks for each lot$-$sizing methods$)$

$(2)$ The product structure diagram for producing item A is given as follows.

The beginning inventory in week $1$ for item B and C are $100$ units and $150$ units respectively. The lead time for

both item B and item C is one week. There are $50$ units of item B scheduled to be received at the beginning of

week $2$ and $100$ units of item C scheduled to be received at the beginning of week $4.$

Suppose A is produced based on the lot$-$for$-$lot method, and B and C are produced in batches with a fixed batch

size of $100$ units and $150$ units respectively. Complete the MRP schedule for A$,$B$,$ and C in the following tables.

$(4$ marks for A; $6$ marks for B;$6$ marks for C $)$