Las ganancias de un negocio se pueden determinar al restar los costos de los ingresos. Supongamos que la ganancia de un negocio son representadas por la función: R(x): 5x-0.01x^2 y los costoa de fabricaa del producto son representados por C(x): 100+2x donde x es el numero de unidades del producto. Determine la función ganancias. Halle una función P(x) que represente las ganancias de la empresa y determine la ganancia máxima.

Función de beneficios = P(x) =-0.01x² + 3x - 100

Ganancias máximos = 125

Y ocurre cuando x = 150 unidades

Profits Function = P(x) = -0.01x² + 3x - 100

Maximum profits = 125

And it occurs when x = 150 units

Step-by-step explanation:

Ganancias = Ingresos - Costos

Ingresos = R (x) = 5x - 0.01x²

Costos = C (x) = 100 + 2x

Función de ganancias = P (x) = R (x) - C (x)

= (5x - 0.01x²) - (100 + 2x)

= 5x - 0.01x² - 100 - 2x

= 3x - 0.01x² - 100

P (x) = -0.01x² + 3x - 100

Para obtener las máximas ganancias, utilizamos el análisis de diferenciación para la función de ganancias.

En el nivel de Ganancias máximo, (dP / dx) = 0 y (d²P / dx²) < 0

P(x) = -0.01x² + 3x - 100

(dP/dx) = -0.02x + 3

Al máximo Ganancias, (dP/dx) = 0

(dP/dx) = -0.02x + 3 = 0

x = (3/0.02) = 150 unidades

Este es el nivel de producto que corresponde a las ganancias máximas.

Para verificar si este es realmente el punto máximo de la función de ganancias,

(dP/dx) = -0.02x + 3

(d²P/dx²) = -0.02 < 0 (lo que demuestra que realmente es el punto de máximo ganancias).

Por lo tanto, la ganancia máxima ocurre cuando x = 150 unidades

P(x) = -0.01x² + 3x - 100

P(x) = -0.01(150²) + 3(150) - 100 = 125

¡¡¡Espero que esto ayude!!!

English Translation

The profits of a business can be determined by subtracting the costs from the income. Suppose that the revenue of a business is represented by the function:

R(x) = 5x - 0.01x²

and the manufacturing costs of the product are represented by

C(x) = 100 + 2x

where x is the number of units of the product. Determine the profits function. Find a function P (x) that represents the profits of the firm and determine the maximum profit.

Solution

Profits = Revenue - Costs

Revenue = R(x) = 5x - 0.01x²

Costs = C(x) = 100 + 2x

Profits function = P(x) = R(x) - C(x)

= (5x - 0.01x²) - (100 + 2x)

= 5x - 0.01x² - 100 - 2x

= 3x - 0.01x² - 100

P(x) = -0.01x² + 3x - 100

To obtain maximum profits, we use differentiation analysis for the profit function.

At the maximum profit level, (dP/dx) = 0 and (d²P/dx²) < 0

P(x) = -0.01x² + 3x - 100

(dP/dx) = -0.02x + 3

At maximum profit, (dP/dx) = 0

(dP/dx) = -0.02x + 3 = 0

x = (3/0.02) = 150 units

This is the product level that corresponds to maximum profits.

To check if this is truly the maximum point of the profit function,

(dP/dx) = -0.02x + 3

(d²P/dx²) = -0.02 < 0 (which shows that it truly is the maximum profit point.

Hence, maximum profit occurs when x = 150 units

P(x) = -0.01x² + 3x - 100

P(x) = -0.01(150²) + 3(150) - 100 = 125

Hope this Helps!!!

step-by-step explanation:

let

we know that

the y-intercept is the y-coordinate of the point when the value of x is equal to zero

so

the y-coordinate of the point a is the y-intercept

the answer part a) is

the value of y-intercept is

part b) find the slope m

we know that

the value of the slope is equal to

substitute the values

therefore

the answer part b) is

the value of the slope is equal to

the general answer is

the slope is

the value of y-intercept is