$100g$ of soaked beans contains $2\mathrm{.}5g$ corn syrup, $50g$ of water and the remaining part consists of solid particles. This solution is mixed with $100g$ of molasses which contains $50g$ of sucrose, $1g$ corn syrup, $18g$ water and the remaining solid particles. Water is added to obtain a diluted corn syrup solution containing $2g$ of inverted sugar per $100g$ of final product. During the process, $125kg$ of soaked beans and $45kg$ of molasses are added per hour.

a$)$ Illustrate the process in a diagram.

b$)$ Formulate the mass balance with appropriate assumptions.

c$)$ Solve for water that needs to be added per hour.

d$)$ Solve for sucrose concentration in the final product.

IMK$106$: Introduction to Food Engineering

Table $1$ is provided to assist in problem solving. You are required to fill in the appropriate items and values as described in the question. Name Flow $1-$Flow $4$ accordingly $($hint: the solution at the inlet and the solution at the outlet$).$

Table $1$: Mass balance for the batch mixing process.

$\backslash$table$[[$Flow$,$In $($kg$/$h$),$Out $($kg$/$h$)],[\backslash$table$[[$Corn$],[$syrup$]],$Sucrose,Solid,Water,Total,$\backslash$table$[[$Corn$],[$syrup$]],$Sucrose,Solid,Water,Total,$],[$Flow $1,,,,,,,,,,,],[$Flow $2,,,,,,,,,,,],[$Flow $3,,,,,,,,,,,],[$Flow $4,,,,,,,,,,,],[$Total$,,,,,,,,,,,]]$

$(20$ marks$)$