q 1. the following data pertains to a given inventory item: demand: 500 units per month ordering cost: $30…

Explanation:

Step1: Calculate annual demand

Annual demand $D = 500\times12=6000$ units.

Step2: Calculate EOQ

The Economic - Order - Quantity (EOQ) formula is $EOQ=\sqrt{\frac{2DS}{H}}$, where $D$ is the annual demand, $S$ is the ordering cost per order, and $H$ is the holding cost per unit per year. Here, $D = 6000$, $S = 30$, and $H = 1$. So, $EOQ=\sqrt{\frac{2\times6000\times30}{1}}=\sqrt{360000}=600$ units.

Step3: Calculate re - order point

The re - order point (ROP) is calculated as $ROP = d\times L$, where $d$ is the daily demand and $L$ is the lead - time. The daily demand $d=\frac{D}{360}=\frac{6000}{360}=\frac{50}{3}$ units per day. The lead - time $L = 1.5$ months. Since the monthly demand is 500 units, the 1.5 - month demand (re - order point) $ROP=500\times1.5 = 750$ units.

Step4: Determine maximum inventory level

The maximum inventory level is equal to the EOQ when there is no safety stock. So, the maximum inventory level is 600 units because, in the basic EOQ model, inventory builds up from zero to the EOQ quantity when an order is received and then depletes over time.

Step5: Calculate annual holding cost

The annual holding cost formula is $HC=\frac{Q}{2}\times H$, where $Q$ is the order quantity (in this case, $Q = EOQ = 600$) and $H$ is the holding cost per unit per year. So, $HC=\frac{600}{2}\times1=300$ dollars.

Answer:

a) 600 units b) 750 units c) 600 units d) $300$