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)

165

likes
826 views

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)

Expert avatar
Birdie
4.5
100 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 $P = -2X + 70$

Frequently asked questions (FAQs)
Find the value of y at x = 3 in the circle with equation x^2 + y^2 = 25.
+
Is it possible for two triangles with sides measuring 5cm, 6cm, and 7cm respectively, to be congruent?
+
What is the integral of (3x^2 - 2x + 5) dx?
+
New questions in Mathematics
A pump with average discharge of 30L/second irrigate 100m wide and 100m length field area crop for 12 hours. What is an average depth of irrigation in mm unIt?
The patient is prescribed a course of 30 tablets. The tablets are prescribed “1 tablet twice a day”. How many days does a course of medication last?
Calculate the equation of the tangent line ay=sin(x) cos⁡(x)en x=π/2
What’s 20% of 125?
(5u + 6)-(3u+2)=
If the midpoint of point A on the x=3 line and point B on the y=-2 line is C(-2,0), what is the sum of the ordinate of point A and the abscissa of point B?
A person borrows rm 1000 from a bank at an interest rate of 10%. After some time, he pays the bank rm 1900 as full and final settlement of the loan. Estimate the duration of his loan.
4x/2+5x-3/6=7/8-1/4-x
There are four times as many roses as tulips in Claire’s garden. Claire picked half of the number of roses and 140 roses were left in the garden. How many roses and tulips were in the Garden the first?
Suppose the Golf ball market is perfectly competitive and the functions are known: Q = 120 – 2Px – 2Py 0.2I Q = 2Px 40 Where I = Consumers' income ($200) and Py = Price of Good Y (40) Calculate the equilibrium elasticity: a) 1.6 b) -6 c) 6 d) 0.6
The ninth term of a given geometric progression, with reason q , is 1792, and its fourth term is 56. Thus, calculate the fourth term of another geometric progression, whose ratio is q +1 and whose first term is equal to the first term of the first P.G. described.
If X1 and X2 are independent standard normal variables, find P(X1^2 + X2^2 > 2.41)
30y - y . y = 144
Determine the increase of the function y=4x−5 when the argument changes from x1=2 to x2=3
Find each coefficient described. Coefficient of u^2 in expansion of (u - 3)^3
A teacher has 25 red and yellow counters altogether. She has 4 times as many red counters than yellow counters. How many yellow counters does the teacher have?
In a laboratory test, it was found that a certain culture of bacteria develops in a favorable environment, doubling its population every 2 hours. The test started with a population of 100 bacteria. After six hours, it is estimated that the number of bacteria will be:
X^X =49 X=?
Find the equation of a straight line that has slope 3 and passes through the point of (1, 7) . Write the equation of the line in general forms
-1/3x+15=18