For the chromatographic separation of fructose and glucose on ion-exchange resin in the calcium form, the equilibrium is linear for concentrations below \(0.05 \mathrm{~g} / \mathrm{ml}\). At \(30^{\circ} \mathrm{C}, \mathrm{q}_{\mathrm{G}}=\) \(0.51 \mathrm{c}_{\mathrm{G}}\) and \(\mathrm{q}_{\mathrm{F}}=0.88 \mathrm{c}_{\mathrm{F}}\) with \(\mathrm{q}\) and \(\mathrm{c}\) in \(\mathrm{g} / \mathrm{ml}\). Properties: \(\varepsilon_{\mathrm{e}}=0.4\) and \(\varepsilon_{\mathrm{p}}=0.0, \mathrm{~L}=100 \mathrm{~cm}\), and \(\mathrm{v}_{\text {super }}=15 \mathrm{~cm} / \mathrm{min}\).

a. Separation of only fructose and glucose.
a1. If a feed pulse \(<1.0 \mathrm{~s}\) in length is input, at what time will the glucose and fructose peaks exit the column?
a2. If there is no zone spreading, what is the longest feed pulse (minutes) that can just separate fructose and glucose?
a3. If a second feed pulse will be introduced for part \(b\), what is the soonest this feed can be introduced while maintaining separation of fructose and glucose?
a4. What \(\%\) of the time can feed be input?

b. Separate fructose and glucose but with a third component with linear equilibrium \(\mathrm{q}_{3}=6\) \(c_{3}\).
b1. If a feed pulse \(<1.0 \mathrm{~s}\) in length is input, at what time will the glucose, fructose, and third component peaks exit the column?
b2. If there is no zone spreading, what is the longest feed pulse (minutes) that can just separate fructose and glucose, and fructose from the third component?
b3. If a second feed pulse will be introduced for part \(b\), what is the soonest this feed can be introduced while maintaining the separation in part \(\mathrm{b}\) ?
b4. What \(\%\) of the time can feed be input?
Part \(\mathrm{b}\) of this problem is an example of the general elution problem.