There are a variety of methods to extract analytes from a solid sample, but the general principles are the same for most methods: find a suitable solvent and determine the experimental conditions—such as time, temperature, and solvent-to-solid ratio—that allow the solvent to extract completely the analytes from the sample. In this section of the case study you will select a solvent and optimize the extraction temperature and the microwave's power; in Part V you will optimize the solvent-to-solid ratio and the extraction time.

Because it is difficult to optimize simultaneously five different variables—in the lingo of method development we call a variable a factor, and we call a factor's value its level—you will complete three one-factor-at-a-time optimizations to identify a solvent and to determine the temperature and the microwave power that maximizes the extraction of Danshen’s constituents [11].

In a one-factor-at-a-time optimization, the level for one factor is varied over a range of values while holding constant the levels of other factors. Each factor is optimized in turn, a process we repeat, if necessary, over multiple cycles until we find the set of factor levels that gives the best response; we call this set of factor levels and its response the system's global optimum.

**Investigation 10.** A one-factor-at-a-time optimization is an effective and an efficient algorithm when the factors behave independently, and an effective, although not necessarily an efficient, algorithm when the factors are dependent. What does it mean to say that two factors are independent or dependent? What does it mean to say that an optimization is efficient or effective? Why do dependent factors generally require that we optimize each factor more than once? Although the choice of solvent, temperature, and microwave power are dependent factors, for this case study we will optimize each factor once only. Explain why this is a reasonable choice. For the analysis in this case study, is the order in which these three factors are optimized important? Why or why not?

[11] You can read more about optimization strategies in general, and one-factor-at-a-time optimizations more specifically, in Chapter 14 of *Analytical Chemistry 2.0.*