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System Modelling - Output and State Differential Equation

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Consider the ice-cream manufacture process shown in the attachment. The ice-cream is made up of the following ingredients:

i) Liquid (cream, milk, water etc.) added at a rate r1 [kg/hr] and with a density p1 [kg/1].
... {see attachment for more details}

(a) Find a model for the process with height in the tank and density of manufactured ice-cream as outputs. Be careful of units. Clearly state any futher assumptions you find necessary.
(b) By considering profit as the difference between cost and income, add a state differential equation to your system to give profit an additional output. The liquid ingredients cost C1 [Rand/litre], the sugar costs C5 [Rand/kg] and the air is free (i.e. negligible compression costs etc.). The selling price of ice-cream is S [Rand/litre].

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Please check the attached file Q36413.doc.