Question

Sarah owns and operates a small factory that manufactures plastic bottles which she sells to bottling companies.

Additional information:
Annual demand is 1 million bottles spread evenly over the year
Setup cost is $5000 per batch
Holding cost is $3 per annum for each bottle
Maximum production capacity is 2 million bottles per annum
Currently, bottles are manufactured in 10 batches
A. Find the optimum production quantity that Sarah should produce to minimize her costs
B. Calculate the current annual holding cost and setup cost​
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Answer 1

The optimum production quantity for Sarah using the EOQ model is approximately 57,735 bottles per batch. Her current annual holding cost is $150,000, and the setup cost is $50,000.

Step-by-step explanation:

Optimum Production Quantity and Costs

To find the optimum production quantity that minimizes costs for Sarah's factory, we use the Economic Order Quantity (EOQ) model:

EOQ = √((2 * Demand * Setup Cost) / Holding Cost)

Plugging in the values provided:

EOQ = √((2 * 1,000,000 bottles * $5,000) / $3 per bottle)

= √((2,000,000 * $5,000) / $3)

= √(10,000,000,000 / 3)

EOQ ≈ 57,735 bottles (rounded to the nearest bottle)

This is the quantity that Sarah should produce per batch to minimize her setup and holding costs.

Now, let's calculate the current annual holding cost and setup cost:

Current Holding Cost = Average Inventory Level * Holding Cost per Bottle

Since Sarah manufactures in 10 batches, the average inventory level is half of the production quantity per batch.

Current Holding Cost = (1,000,000 bottles / 10 batches / 2) * $3

= 50,000 bottles * $3

= $150,000

Current Setup Cost = Number of Batches * Setup Cost per Batch

Current Setup Cost = 10 batches * $5,000

= $50,000

Therefore, Sarah's current annual holding cost is $150,000, and the setup cost is $50,000.