Questions: Inventory control. A publishing company sells 50,000 copies of a certain book each year. It costs the company 1 to store a book for one year. Each time that it prints additional copies, it costs the company 1,000 to set up the presses. How many books should the company produce during each printing in order to minimize its total storage and setup costs?

Inventory control. A publishing company sells 50,000 copies of a certain book each year. It costs the company 1 to store a book for one year. Each time that it prints additional copies, it costs the company 1,000 to set up the presses. How many books should the company produce during each printing in order to minimize its total storage and setup costs?

Transcript text: 39. Inventory control. A publishing company sells 50,000 copies of a certain book each year. It costs the company $\$ 1$ to store a book for one year. Each time that it prints additional copies, it costs the company $\$ 1,000$ to set up the presses. How many books should the company produce during each printing in order to minimize its total storage and setup costs?

Solution

Solution Steps

Step 1: Calculate the Economic Order Quantity (EOQ)

The EOQ formula is given by: $$ EOQ = \sqrt{\frac{2 \times S \times C_p}{C_s}} $$ where:

$S$ is the annual sales volume = 50000
$C_p$ is the setup cost for printing = 1000
$C_s$ is the storage cost per book per year = 1 Plugging in the values, we get: $$ EOQ = \sqrt{\frac{2 \times 50000 \times 1000}{1}} = 10000 $$

Step 2: Round the EOQ to the nearest whole number

Since it's not practical to produce a fraction of a book, the EOQ of 10000 is rounded to the nearest whole number, which is 10000.

Final Answer:

The optimal number of books to print in each batch to minimize the total cost, considering both the storage cost per book and the setup cost for printing, is 10000 books.

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