$($a$)$ Evaluate three M$/$P policies and determine the Profit Per Cycle $($PPC$).$ Note that

PPC $=$ Sales Revenue$-($Fixed Promotion Cost $+$ Inventory Cost $+$ Manufacturing Cost$)$

$($b$\mathrm{.}1)$ Based on observations from the production department, it is noted that $5\%$ of the produced items are defective and need to be discarded, resulting in a yield rate of $95\%().$ For instance, to fulfill a demand of $10$ units, one must produce X$0\mathrm{.}95=10,$ which implies X$=10\mathrm{.}527$ units. This ensures that $(10\mathrm{.}527)(0\mathrm{.}95)=10$ units meet the demand. Now, assess the $(1)$ High Promotion policy and determine the PPC$.$ Explain the cost of bad production quality. $($Note that over the first $8$ weeks, the part supplier consistently delivers $5,000$ units of essential components per week, resulting in a total of $40,000$ parts supplied during the $8-$week period.$)$

$($b$\mathrm{.}2)$ Based on the observations from the production department, $5\%$ of the products produced are defective and require rework. It is also assumed that only one rework $($which means a total of $2$ visits$)$ is needed to rectify the defective item. Now, evaluate the $(1)$ High Promotion policy and calculate the PPC$.$ Explain the cost of bad production quality.