$1)$ What are the five basic inputs to the manufacturing planning and control system?$$

$2)$ If the cost of manufacturing $($direct material and direct labor$)$ is $60\%$ of sales and profit is $10\%$ of sales, what would be the improvement in profit if$,$ through better planning and control, the cost of manufacturing was reduced from $60\%$ of sales to $50\%$ of sales?$$

$3)$ On average, a firm has an $8-$week lead time for work$-$in$-$process, and annual cost of goods sold is $$12$ million. Assuming that the company works $50$ weeks a year:$$

$$ a$)$ What is the dollar value of the work$-$in$-$process?$$

$$ b$)$ If the lead time would be reduced to $6$ weeks, what would be the reduction in WIP?$$

$4)$ Define the following:$$

$$a$)$ Master Production Scheduling $($MSP$)$

$$b$)$ Material Requirements Plan $($MRP$)$

$$c$)$ Sales and operations planning $($S&OP$)$

$5)$ If the opening inventory is $400$ units, demand is $900$ units, and production is $700$ units, what will be the ending inventory?$$

$6)$ A company wants to produce $480$ units over the next three months at a uniform rate. The months have $19,20,$ and $21$ working days, respectively. On average, how much should the company produce each day to level production?$$

$7)$ If the opening backlog is $450$ units, forecast demand is $700$ units, and production is $800$ units, what will be the ending backlog?$$

$8)$ What four functions does the master production schedule $($MPS$)$ perform in the production planning system?$$

$9)$ What would happen if the planning horizon for the master schedule were too short? Why?$$

$10)$ What is the purpose of rough cut capacity?