Step 1 :Given two points on the demand curve: (25, 150) and (35, 100), we can find the equation of the line passing through these points, which will give us the demand as a function of price.
Step 2 :Then we can find the revenue as a function of price by multiplying the price by the demand.
Step 3 :The maximum revenue will occur at the vertex of this parabola, which we can find by completing the square or by using the formula for the vertex of a parabola.
Step 4 :By solving the equation, we find that the critical point is at \(p = 27.5\).
Step 5 :Substituting \(p = 27.5\) into the revenue equation, we find that the maximum revenue is \(3781.25\).
Step 6 :Final Answer: The maximum revenue is achieved when the price per dozen is \(\boxed{27.50}\) dollars, and the maximum revenue is \(\boxed{3781.25}\) dollars.