We are dealing with an inventory problem where the storage cost depends on the maximum inventory size, rather than the average. The goal is to determine the optimal quantity $q$ to print per run that minimizes total costs.

The formula for the optimal order quantity $q^*$ in this setting is:
$q^* = \sqrt{\frac{2 \cdot f \cdot M}{k}}$ where:

• $f$ = Fixed setup cost per run ($1200)
• $M$ = Annual demand (5600 copies)
• $k$ = Storage cost per unit ($4 per book stored)

Step 1: Substituting known values into the formula

Given:

• $f = 1200$
• $M = 5600$
• $k = 4$

$q^* = \sqrt{\frac{2 \cdot 1200 \cdot 5600}{4}}$

Step 2: Simplifying the expression inside the square root

$2 \cdot 1200 \cdot 5600 = 13,440,000$ $\frac{13,440,000}{4} = 3,360,000$

Step 3: Calculating the square root

$q^* = \sqrt{3,360,000} = 1833.33$

Since the number of books must be a whole number, we round it to 1833 books per run.

Step 4: Conclusion

The optimal number of books to print per print run is approximately 1833 books.

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Would you like further clarifications or additional insights?

Here are 5 related questions you might find useful:

1. How does this solution change if the storage cost depends on the average inventory?
2. What if the fixed setup cost increases? How would that impact the optimal print run size?
3. How do we calculate the total annual cost with this order quantity?
4. What happens if the demand increases to 10,000 books per year?
5. How would we handle non-negligible per-unit production costs in this calculation?

Tip: The formula used here is a variation of the Economic Order Quantity (EOQ) model, with modifications for maximum inventory cost.