Hi Marco,
After looking more closely at the model you provided, I think I know why we are having a hard time communicating about this.
The model you shared is this one from the profiler documentation. It is meant to show how to use the simulator to add uncertainty to the input factors and see the likely range of outcomes.
The question that started this discussion was “How to optimize factors with uncertainty in one step?” The answer is, as @Mark_Bailey suggested at the outset, the same with or without uncertainty in the factors: simply set and maximize the desirability function for profit. When you follow that procedure for this example, JMP suggests that you should have high unit sales, high unit price, and low unit cost to maximize profit. (Let’s ignore that this simplified model omits the relationship between unit price and unit sales, a.k.a. supply and demand). You didn’t even need to use the profiler to arrive at this conclusion, it should be obvious from the equation.
So what good is it to add uncertainty to the factors? What extra insight does that give you? Used in conjunction with the simulator, it allows you to forecast what the likely outcomes will be at a given set of factor settings. It’s not about optimization. It’s about helping you understand the implications of optimization that you performed previously.
It’s true that there is some subtlety about choosing between factor settings that maximize the mean expected profit and those that minimize the variability of expected profit, and those considerations might lead you to use the design space profiler and/or the simulation experiment features in JMP. But I think those considerations are not what you were really asking about.