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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

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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

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Rasheed
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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}

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