\section*{Task 1 - 041011}

In a company where electric motors are assembled, the acquisition of a new conveyor belt system, which costs 105000 MDN, can reduce the labor costs per motor by 0.50 MDN and the overhead costs by 8800 MDN annually.

a) How many motors must be assembled annually at a minimum for the costs of the new system to be covered by the savings in wages and overhead costs within three years? b) How many motors must be assembled annually at a minimum for an additional annual profit of 10000 MDN to be achieved on top of that?
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a) If \(x\) engines are assembled per year, then \(0.50 \cdot x + 8800\) MDN are saved per year. For the costs of the plant to be covered after three years, it must hold that \(3 \cdot (0.5 \cdot x + 8800) = 105000 \Rightarrow x = 52400\).

b) Of the 105000 MDN, 35000 MDN must be saved annually, and in addition, there should be an additional profit of 10000 MDN, so it follows: \(35000 + 10000 = 0.5 \cdot x + 8800 \Rightarrow x = 72400\). At least 72400 engines must be assembled annually.

Solution adopted from \([5]\)