$D(x)$ is the price, in dollars per unit, that consumers are willing to pay for $x$ units of an item, and $S(x)$ is the price, in dollars per unit, that producers are willing to accept for $x$ units. Find (a) the equilibrium point, (b) the consumer surplus at the equilibrium point, and (c) the producer surplus at the equilibrium point.
\[
D(x)=3000-10 x, S(x)=2000+15 x
\]

Step 1 ：Given the demand function \(D(x) = 3000 - 10x\) and the supply function \(S(x) = 2000 + 15x\), we need to find the equilibrium point, the consumer surplus at the equilibrium point, and the producer surplus at the equilibrium point.

Step 2 ：The equilibrium point is the point where the demand equals the supply, i.e., \(D(x) = S(x)\). We can find this point by setting the two equations equal to each other and solving for \(x\).

Step 3 ：Solving \(3000 - 10x = 2000 + 15x\) gives us \(x = 40\). Substituting \(x = 40\) into either the demand or supply function gives us the equilibrium price. For example, \(D(40) = 3000 - 10*40 = 2600\). So, the equilibrium point is at \((40, 2600)\).

Step 4 ：The consumer surplus is the area between the demand curve and the price level up to the quantity demanded. It can be calculated as the integral of the demand function from 0 to the quantity demanded minus the total amount the consumers are paying. Calculating this gives us a consumer surplus of \(8000\) dollars.

Step 5 ：The producer surplus is the area between the supply curve and the price level up to the quantity supplied. It can be calculated as the total amount the producers are receiving minus the integral of the supply function from 0 to the quantity supplied. Calculating this gives us a producer surplus of \(12000\) dollars.

Step 6 ：Final Answer: The equilibrium point is at \((40, 2600)\). The consumer surplus at the equilibrium point is \(\boxed{8000}\) dollars and the producer surplus at the equilibrium point is \(\boxed{12000}\) dollars.