This Demonstration calculates the mass of three food ingredients that will form a mixture of a chosen mass having a specified moisture content and amount of carbohydrates, fat or protein (CFP), etc. Each ingredient is specified by its percent moisture and percent CFP. The calculation is based on three mass balances: the total mass, the moisture and the CFP. If there is exactly one, solution the numerical results are displayed in a table. The proportion of each component in the mixture is also displayed in a pie chart along with two other pie charts that illustrate how much each ingredient contributes to the mixture's moisture and CFP.
Mixing ingredients is a common operation in the food and other industries. The target mixture is usually specified by the total mass, the moisture content and the concentration of an important component. This Demonstration calculates the amounts of three components needed to meet these specifications. The calculation is based on the solution of three mass-balance equations: total mass (arbitrary units), moisture contents (%) and the important component (%) (carbohydrates, fat or protein (CFP), etc., for example). They are:
where a, b, and c are the three ingredients, and the moistures and CFPs are the user-entered values (in percent). The three unknowns are the masses of the ingredients , , and .
When these equations have unique solutions, the values of , , and are displayed in a table along with their contribution to the mixture in percent. The solution is also displayed as a pie chart accompanied by two smaller pie charts depicting each component's percent contribution to the mixture's moisture and CFP.
When the equations at a particular set of parameters do not have a unique solution or yield a physically impossible or unrealistic situation, an error message is displayed in place of the table and pie charts.