Question

Disponemos de 210000 euros para invertir en la bolsa. Nos recomiendan dos tipos de acciones. Las del tipo A que rinden el 10% y las del tipo B que rinde el 8%. Decidimos invertir un máximo de 130000 euros en las del tipo A y como mínimo 6000 euros en las del tipo B. Además queremos que la inversión en las del tipo A sea menor o igual que el doble de la inversión B. ¿Cual tiene que ser la distribución de la inversión para obtener el máximo interés anual?

Answer 1

To obtain the maximum annual interest, the optimal distribution is to invest 130000 euros in type A stocks and 65000 euros in type B stocks.

To obtain the maximum annual interest, we need to determine the optimal distribution of the investment between type A and type B stocks. Let's assume x euros are invested in type A stocks and y euros are invested in type B stocks.

Based on the given conditions:

The investment in type A stocks should be less than or equal to twice the investment in type B stocks: x ≤ 2y

The maximum investment in type A stocks is 130000 euros: x ≤ 130000

The minimum investment in type B stocks is 6000 euros: y ≥ 6000

To maximize the interest, we need to maximize the investment in type A stocks, as they have a higher 10% return compared to the 8% return of type B stocks.

With these conditions, the optimal distribution is:

x = 130000 euros (maximum investment in type A)

y = 65000 euros (half of the investment in type A)