company knows that unit cost $C(x)$ and unit revenue $R(x)$ from the production and sale of $x$ units are related by $C(x)=\frac{[R(x)]^{2}}{88,000}+8782$. Find the rate of change of revenue per unit when the cost per it is changing by $\$ 10$ and the revenue is $\$ 2,000$. Round to the nearest cent.
A. $\$ 878.20 /$ unit
B. $\$ 100.00 /$ unit
C. $\$ 220.00 /$ unit
D. $\$ 549.10 /$ unit

Step 1 ：Given the relationship between unit cost $C(x)$ and unit revenue $R(x)$, we have $C(x)=\frac{[R(x)]^{2}}{88,000}+8782$.

Step 2 ：Taking the derivative of both sides with respect to $x$, we get $\frac{dC}{dx}=\frac{2R(x)\cdot \frac{dR}{dx}}{88,000}$.

Step 3 ：We are asked to find the rate of change of revenue per unit, $\frac{dR}{dx}$, when the cost per unit is changing by $\$ 10$ and the revenue is $\$ 2,000$.

Step 4 ：Substituting $\frac{dC}{dx}=10$ and $R(x)=2000$ into the equation, we get $10=\frac{2\cdot 2000\cdot \frac{dR}{dx}}{88,000}$.

Step 5 ：Solving for $\frac{dR}{dx}$, we get $\frac{dR}{dx}=\frac{10\cdot 88,000}{2\cdot 2000}=\boxed{\$ 220.00 / \text{unit}}$.