Answered: a) Develop a mathematical model for the…

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter2: Introduction To Spreadsheet Modeling

Section: Chapter Questions

Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...

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Question

Consider the mixing process shown in the figure. A mixing chamber initially contains 4 liters of a clear liquid. Clear liquid flows into the chamber at a rate of 10 liters per minute. A dye solution having a concentration of 0.25 kilograms per liter is injected into the mixing chamber at a constant rate of liters per minute. When the mixing process is started, the well-stirred mixture is pumped from the chamber at a rate of 10 + r liters per minute.

(a) Develop a mathematical model for the mixing process. Let Q represent the amount of dye in kilograms in the mixture.

(dQ/dt)=?

(b) The objective is to obtain a dye concentration in the outflow mixture of 0.1 kilograms per liter. What injection rate r is required to achieve this equilibrium solution?

r = ?

Would this equilibrium value of r be different if the fluid in the chamber at time t=0 contained some dye? yes, no or maybe?

(c) Assume the mixing chamber contains 4 liters of clear liquid at time t. How many minutes will it take for the outflow concentration to rise to within 2% of the desired concentration of 0.1 kilograms per liter?

t=?