Find the consumers' surplus and the producers' surplus at the equlibrium level for the given price-demand and price-supply equations. Include a graph that identifies the consumers' surplus and the producers' surplus. Round all values to the nearest integer.
\[
p=D(x)=54.9-0.09 x ; p=S(x)=15+0.1 x
\]

The value of $x$ at equilibrium is $\square$.
The value dip at equilibrium is $\$ \square$.
The consumers' surplus at equilibrium is $\$ \square$.

Step 1 ：First, we need to find the equilibrium point. The equilibrium point is where the demand equals the supply, i.e., where the price-demand equation equals the price-supply equation. So, we need to solve the equation \(54.9-0.09x = 15+0.1x\) for \(x\). This will give us the quantity at equilibrium.

Step 2 ：Next, we need to find the price at equilibrium. We can do this by substituting the quantity at equilibrium into either the price-demand or price-supply equation.

Step 3 ：Finally, we can calculate the consumers' surplus and the producers' surplus. The consumers' surplus is the area between the price-demand curve and the price line from \(x=0\) to the quantity at equilibrium. The producers' surplus is the area between the price-supply curve and the price line from \(x=0\) to the quantity at equilibrium.

Step 4 ：We can calculate these areas using the formula for the area of a triangle: \(1/2 * base * height\). The base is the quantity at equilibrium and the height is the difference between the price at equilibrium and the price at \(x=0\).

Step 5 ：Final Answer: The value of \(x\) at equilibrium is \(\boxed{210}\). The value dip at equilibrium is \(\$ \boxed{36}\). The consumers' surplus at equilibrium is \(\$ \boxed{1985}\). The producers' surplus at equilibrium is \(\$ \boxed{2205}\).