Example $2$:

In a manufacturing company, a material is used as follows:

Maximum consumption $-12,000$ units per week

Minimum consumption $-4,000$ units per week

Normal consumption $-8,000$ units per week

Re$-$order quantity $-48,000$ units

Time required for Delivery$-$Minimum: $4$ weeks, Maximum: $6$ weeks

Maximum reorder period for emergency purposes is $2$ weeks

Calculate: $($a$)$ Re$-$order level; $($b$)$ Minimum level; $($c$)$ Maximum level; $($d$)$ Danger level; and $($e$)$ Average stock level.