suppose a products revenue function is given by $r(q)=-6q^{2}+1000q$, where $r(q)$ is in dollars and $q$ is…

suppose a products revenue function is given by $r(q)=-6q^{2}+1000q$, where $r(q)$ is in dollars and $q$ is units sold. find a numeric value for the marginal revenue at 45 units. $mr(45)=square$ $ per unit

suppose a products revenue function is given by $r(q)=-6q^{2}+1000q$, where $r(q)$ is in dollars and $q$ is units sold. find a numeric value for the marginal revenue at 45 units. $mr(45)=square$ $ per unit

Answer

Explanation:

Step1: Recall marginal - revenue formula

The marginal revenue function $MR(q)$ is the derivative of the revenue function $R(q)$. Given $R(q)=-6q^{2}+1000q$, using the power - rule $\frac{d}{dq}(ax^{n})=nax^{n - 1}$, we have $MR(q)=\frac{dR(q)}{dq}$. $MR(q)=\frac{d}{dq}(-6q^{2}+1000q)=-12q + 1000$.

Step2: Evaluate marginal revenue at $q = 45$

Substitute $q = 45$ into the marginal revenue function $MR(q)$. $MR(45)=-12\times45 + 1000$. $MR(45)=-540+1000$. $MR(45)=460$.

Answer:

$460$