Final answer:
To achieve a profit objective of 40,000 Euros, Herr Zeitgeist must sell 7,000 watches, taking into account his production costs and advertising expenses. None of the provided options are correct.
Step-by-step explanation:
The student is asking a break-even analysis and profit calculation question in Mathematics to determine how many watches must be sold to achieve a certain profit objective.
To find the answer, we need to first calculate the total cost to produce one watch, including the cost of watch faces from Italy, mechanisms from Spain, assembly in Portugal, and the proportional cost of advertising for one watch.
Then we need to subtract this total cost from the selling price of one watch to find the profit per watch, and finally, divide the profit objective by the profit per watch to find the number of watches Herr Zeitgeist needs to sell.
To calculate the cost per watch:
- Cost of watch face: 5 Euros
- Cost of mechanism: 15 Euros
- Cost of assembly: 10 Euros
Total cost per watch is 5 + 15 + 10 = 30 Euros.
We also need to consider the advertising cost. Since it is a fixed cost, it will be divided among the number of watches sold. However, the exact number of watches is what we are trying to find, so we will include the advertising cost later in the calculation.
Herr Zeitgeist sells each watch for 50 Euros and aims to earn 40,000 Euros in profit. The profit per watch is the selling price minus the cost per watch:
Profit per watch = 50 Euros (selling price) - 30 Euros (total cost per watch) = 20 Euros
To calculate the number of watches to sell to reach the profit objective without considering advertising costs:
Number of watches = Profit objective / Profit per watch
Number of watches = 40,000 Euros / 20 Euros per watch = 2,000 watches
However, once we consider the advertising costs, the actual number of watches needed to break even is higher, since the advertising costs need to be recovered as well. We need to add the advertising costs to the profit objective to find the total amount of money needed:
Total amount needed = Profit objective + Advertising costs
Total amount needed = 40,000 Euros + 100,000 Euros = 140,000 Euros
Therefore, the adjusted number of watches to sell to reach the total amount needed:
Adjusted Number of watches = Total amount needed / Profit per watch
Adjusted Number of watches = 140,000 Euros / 20 Euros per watch = 7,000 watches
Hence, none of the provided options (a) 800 watches, (b) 1,200 watches, (c) 1,600 watches, (d) 2,000 watches are correct. Herr Zeitgeist must sell 7,000 watches to meet his profit objective including the advertising costs.