To determine the purchase price up to which it is more profitable to buy the zippers rather than manufacture them, we compare the total cost of manufacturing the zippers in-house with the total cost of purchasing them.
1. The total cost to manufacture zippers for 75,000 jackets is:
\text{Total Manufacturing Cost} = \text{Fixed Costs} + (\text{Variable Cost per Zipper} \times \text{Number of Jackets}) = 45,000 \text{ euros}
2. The total cost to purchase zippers for 75,000 jackets at €0.80 per unit would be:
\text{Total Purchase Cost} = \text{Purchase Price per Zipper} \times \text{Number of Jackets} = 0.80 \times 75,000 = 60,000 \text{ euros}
3. To find the purchase price per zipper for equal cost-effectiveness, set the total manufacturing cost equal to the total purchase cost:
45,000 = P \times 75,000
4. Solve for P to find the purchase price per zipper:
P = \frac{45,000}{75,000} = 0.60 \text{ euros}
Therefore, up to a purchase price of €0.60 per zipper, it is more profitable for the company to buy the zippers rather than manufacture them.
\boxed{P = 0.60 \text{ euros}}