How would you decide on the range, a and b, of the dependent variable x, to satisfy the desired value (tolerated value) of the error criterion calculated based on the square root of Pi number? That means you have a single variable x, of which the range is to be optimized, and controlled to satisfy the error criterion, calculated based on the area under the curve of the function f(x)=exp(x2). The integral of the function f(x)=exp(x2) from to +, is equal to the square root of Pi number. We need to decide on the range of the dependent variable x (or variables), to be optimized (or to be manipulated or to be controlled). Question 2: What is the purpose of using the set point value from the process control point of view? Similar to the optimization, the same approach can be used for process control to decide on the range of the manipulated variables in order to keep the control variables within an acceptable range (or in simple words, the set point). In other words, what should be done if the set point is a distribution itself? What would you use instead of the set point value if the system to be controlled or optimized have distributions varying with time and location as the production, process, system or life continues? The objective is to satisfy the desired error. The optimization variable is the range from a to b (or interval from a to b ) of x. How do you decide on Question 3: What are the constraints? The area under the curve for a range of x, cannot be smaller than zero and also cannot be greater than the square root of Pi number. f(x)=ex20