For the final question, assume that the peak of the normal distribution is at the same position as the peak of the actual data (i.e., at = 1.8 mol/m^3). Thanks!

A blending process, shown in Figure Q2.7, mixes component A into a stream. The objective is to maximize the amount of A in the stream without exceeding the upper limit of the concentration of A, which is 2.2 mole/m3. The current operation is open-loop, with the operator occasionally look- ing at the analyzer value and changing the flow of A. The flow during the period that the data was collected was essentially constant at 1053 m/h. How much more A could have been blended into the stream with perfect control, that is, if the concentration of A had been maintained exactly at its maximum? What would be the improvement if the new distribution were normal with a standard deviation of 0.075 mole/m3? Pure A Solvent Blended stream AI) Historical data -Limiting value 0.3 0.25 0.2 Frequency 0.15 0.1 0.05 0 1.5 1.6 1.7 1.8 1.9 2.0 2.1 Concentration of A in blend, moles/m3 FIGURE Q2.7 Consider further the system Suppose that it were possible to develop a process with frequency data that possessed a normal distribution with a peak at 1.9 mol/m and a standard deviation of 0.1 mol/m. Would this process satisfy soft or hard safety constraints? What is the projected improvement in output over the actual data