Question

The marginal revenue function of a company is given by: dR/dq=4000-16q-6q^2 find the income function, knowing that if there is no production the income is zero

175

likes
873 views

Answer to a math question The marginal revenue function of a company is given by: dR/dq=4000-16q-6q^2 find the income function, knowing that if there is no production the income is zero

Expert avatar
Rasheed
4.7
105 Answers
Para encontrar la función de ingreso, primero debemos integrar la función de ingreso marginal dada:

\frac{dR}{dq} = 4000 - 16q - 6q^2

Integrando esta expresión con respecto a q, obtenemos la función de ingreso (R(q)):

\begin{aligned}R(q) &= \int (4000 - 16q - 6q^2) \,dq \&= 4000q - 8q^2 - 2q^3 + C \end{aligned}

Dado que se nos dice que si no hay producción el ingreso es cero, podemos encontrar el valor de la constante C:

Cuando q = 0, R(0) = 0:
0 = 4000(0) - 8(0)^2 - 2(0)^3 + C
0 = C

Por lo tanto, la función de ingreso es:
R(q) = 4000q - 8q^2 - 2q^3

\boxed{R(q) = 4000q - 8q^2 - 2q^3}

Frequently asked questions (FAQs)
Math Question: What is the limit of (3x^2 + 4x + 7) as x approaches 2?
+
Find the limit as x approaches 0 of (sinx/x) using L'Hospital's Rule.
+
What is the product of 497 and 26?
+
New questions in Mathematics
1 + 1
How much volume of water in MegaLiters (ML) is required to irrigate 30 Hectare crop area with depth of 20mm?
Two fire lookouts are 12.5 km apart on a north-south line. The northern fire lookout sights a fire 20° south of East at the same time as the southern fire lookout spots it at 60° East of North. How far is the fire from the Southern lookout? Round your answer to the nearest tenth of a kilometer
a ferry travels 1/6 of the distance between two ports in 3/7 hour. The ferry travels at a constant rate. At this rate, what fraction of the distance between the two ports can the ferry travel in one hour.
-6n+5=-13
The actual length of an object is 1.3 m . If the blueprint uses a scale of 1 : 12 , what is the length of the line on the drawing?
(2b) to the 1/4th power. Write the expression in radical form.
The durability of a tire of a certain brand is a Normal random variable with an average of 64,000 km and a standard deviation of 9,000 km. Assuming independence between tires, what is the probability that the 4 tires on a car will last more than 58,000 km?
Log5 625
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.
DuocUC 2) The cost C, in pesos, for the production of x meters of a certain fabric can be calculated through the function: (x+185) C(x)=81300-6x+ 20000 a) It is known that C(90) 5.344. Interpret this result. (2 points) b) Calculate C'(x) (2 points) 3 x²+111x-0.87 20000 2000 c) Function C calculates the cost while producing a maximum of 500 meters of fabric. Determine the values of x at which the cost of production is increasing and the values of x at which the cost is decreasing. (3 points) d) If a maximum of 500 meters of fabric are produced, what is the minimum production cost? (
Use the power rule for logarithms to solve the following word problem exactly. If you invest $1, 000 at 5% interest compounded annually, how many years will it take before you have $2,000?
Determine the increase of the function y=4x−5 when the argument changes from x1=2 to x2=3
If a|-7 and a|9, then a|-63
Find the zero of the linear function 8x + 24 = 0
prove that for sets SS, AA, BB, and CC, where AA, BB, and CC are subsets of SS, the following equality holds: (A−B)−C=(A−C)−(B−C)
a coffee shop has 9 types of creamer and 11 types of sweetener. In how any ways can a person make their coffee?
Paola went on vacation for 15 days if it rained 20% of the days. How many days did it rain?
Hola👋🏻 Toca en "Crear Nueva Tarea" para enviar tu problema de matemáticas. ¡Uno de nuestros expertos comenzará a trabajar en ello de inmediato!
The car with an irresponsible driver starts to brake when it goes through a red light. When passing the traffic light, he does so at a speed of 115 kph in the right lane. Further ahead, 70 meters from the traffic light, a child is crossing the street and falls. If the effect of the car's brakes is equivalent to a deceleration of magnitude 5.7m/s². Is the child hit by the car or not? How far from the traffic light does the car stop?