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# A jacket manufacturing company is considering making the zippers or purchasing them from another company. If you buy them, it will be for a price of €0.80 per unit. Manufacturing them would entail fixed costs of €30,000 and a variable cost of €0.20 per zipper. It is asked: Assuming that you manufacture 75,000 jackets, up to what purchase price will it be more profitable to buy the zippers? 45,000 euros 35,000 euros 37,500 euros

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## Answer to a math question A jacket manufacturing company is considering making the zippers or purchasing them from another company. If you buy them, it will be for a price of €0.80 per unit. Manufacturing them would entail fixed costs of €30,000 and a variable cost of €0.20 per zipper. It is asked: Assuming that you manufacture 75,000 jackets, up to what purchase price will it be more profitable to buy the zippers? 45,000 euros 35,000 euros 37,500 euros

Gene
4.5
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}}

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