Question

A merchant can sell 20 electric shavers a day at a price of 25 each, but he can sell 30 if he sets a price of 20 for each electric shaver. Determine the demand equation, assuming it is linear. Consider (P= price, X= quantity demanded)

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Answer to a math question A merchant can sell 20 electric shavers a day at a price of 25 each, but he can sell 30 if he sets a price of 20 for each electric shaver. Determine the demand equation, assuming it is linear. Consider (P= price, X= quantity demanded)

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Birdie
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98 Answers
Para determinar la ecuación de la demanda, necesitamos encontrar la relación entre el precio (P) y la cantidad demandada (X).

Primero, vamos a utilizar los datos proporcionados. Sabemos que cuando el precio es de 25, la cantidad demandada es de 20. Y cuando el precio es de 20, la cantidad demandada es de 30.

Podemos usar estos dos puntos para determinar la pendiente de la ecuación de la demanda. La pendiente se calcula utilizando la fórmula:

m = \frac{{Y_2 - Y_1}}{{X_2 - X_1}}

Donde (X1, Y1) y (X2, Y2) son los puntos dados. En nuestro caso, podemos usar los puntos (25, 20) y (20, 30):

m = \frac{{30 - 20}}{{20 - 25}} = \frac{{10}}{{-5}} = -2

Ahora que tenemos la pendiente (-2), podemos utilizarla junto con uno de los puntos para encontrar la ecuación de la demanda en la forma punto-pendiente:

y - y_1 = m(x - x_1)

Usaremos el punto (25, 20) como (x1, y1):

y - 20 = -2(x - 25)

Simplificando la ecuación, obtenemos:

y - 20 = -2x + 50

Finalmente, podemos reorganizar la ecuación para obtener la forma más común de una ecuación lineal:

y = -2x + 70

Por lo tanto, la ecuación de la demanda lineal es:

P = -2X + 70

\textbf{Respuesta:} La ecuación de la demanda lineal es $P = -2X + 70$

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