Given: ( $x$ is number of items) Demand function: $d(x)=300-0.4 x$ Supply function: $s(x)=0.4 x$ Find the equilibrium quantity: Find the consumers surplus at the equilibrium quantity:

Step 1 ：Given the demand function \(d(x) = 300 - 0.4x\) and the supply function \(s(x) = 0.4x\), we need to find the equilibrium quantity and the consumer's surplus at the equilibrium quantity.

Step 2 ：The equilibrium quantity is found when the demand function equals the supply function. That is, we need to solve the equation \(d(x) = s(x)\) for \(x\).

Step 3 ：Solving the equation gives us \(x = 375\). Therefore, the equilibrium quantity is \(375\).

Step 4 ：To find the consumer's surplus at the equilibrium quantity, we calculate the area under the demand curve and above the price (which is the equilibrium price). The consumer surplus is given by the formula \(\frac{1}{2} \times base \times height\).

Step 5 ：The base is the equilibrium quantity and the height is the difference between the maximum price a consumer is willing to pay (which is the y-intercept of the demand function) and the equilibrium price.

Step 6 ：Substituting the values, we get the consumer surplus as \(28125\).

Step 7 ：Final Answer: The equilibrium quantity is \(\boxed{375}\) and the consumer's surplus at the equilibrium quantity is \(\boxed{28125}\).