Solve the problem.
-A company knows that the unit cost $C$ and the unit revenue $R$ from the production and sale of $x$ units are related by $\mathrm { C } = \frac { \mathrm { R } ^ { 2 } } { 122,000 } + 11,397$. Find the rate of change of unit revenue when the unit cost is changing by $\$ 11 /$ unit and the unit revenue is $\$ 1000$.
A) $\$ 671.00 /$ unit
B) $\$ 55.00 / u n i t$
C) $\$ 905.35 /$ unit
D) $\$ 1139.70 /$ unit

Question

Quizplus · Accepted Answer

Given the relationship $C = \frac{R^2}{122,000} + 11,397$, we differentiate both sides with respect to $x$ to find the rate of change of $C$ with respect to $R$. This gives us $\frac{dC}{dR} = \frac{2R}{122,000}$. We are given that $\frac{dC}{dx} = 11$ and $R = 1000$, so substituting $R = 1000$ into our derivative gives $\frac{dC}{dR} = \frac{2(1000)}{122,000} = \frac{2000}{122,000} = \frac{1}{61}$. Since $\frac{dC}{dx} = 11$, we have $11 = \frac{dC}{dR} \cdot \frac{dR}{dx} = \frac{1}{61} \cdot \frac{dR}{dx}$, solving for $\frac{dR}{dx}$ gives $\frac{dR}{dx} = 11 \cdot 61 = 671$. Therefore, the rate of change of unit revenue when the unit cost is changing by $11/unit and the unit revenue is $1000 is $671/unit.

Solve the Problem CCC And the Unit Revenue RRR From the Production and Sale Of

Solve the Problem $C$ And the Unit Revenue $R$ From the Production and Sale Of