The popularity of orange juice, especially as a breakfast drink, makes it an important factor in the economy of orange$-$growing regions.

Marketed juice has either gone through a process in which it was concentrated, or it may be a not$-$from$-$concentrate juice. Frozen

concentrated juice is reconstituted before consumption. Although concentrated juices are less popular in the United States than at

one time, they still have a major segment of the market.

The approaches to concentrating orange juice include evaporation, freeze concentration, and reverse osmosis. Here we examine the

evaporation process by focusing only on two constituents in the juice: solids and water.

Fresh orange juice contains approximately $10\mathrm{.}0wt\%$ solids $($sugar$,$ citric acid and other indigenous ingredients$)$ and frozen concentrate

contains approximately $45\mathrm{.}0wt\%$ solids. The frozen concentrate is obtained by evaporating water from the fresh juice to produce a

mixture that is approximately $63\mathrm{.}0wt\%$ solids. However, so that the flavor of the concentrate will closely approximate that of fresh

juice, the concentrate from the evaporator is blended with fresh orange juice $($and other minor additives$)$ to produce a final

concentrate that is approximately $45\mathrm{.}0$ wt $\%$ solids.

Assume a basis of $300\mathrm{.}0$ kg of fresh juice fed to the process.

Degrees of Freedom

Mass of Concentrate

Bypass Fraction

What is the fraction of fresh juice that bypasses the evaporator?