Evaluating Dissolved Oxygen Dynamics in Fresh Water Fish Tank Using the Modified Cobb Douglas Approach

Abstract

A modified Cobb Douglas model was used to evaluate dissolved oxygen dynamics in a fibre glass fish tank with Chicken Manure as the treatment. Though the model was originally modeled to handle two input variable with their output elasticities, this study looked at seven input variables which includes pH, Temperature, Turbidity, Ammonia, Transparency, TDS (Total dissolved solid), EC (Electrical conductivity) to effectively predict the DO (output). The ANOVA approach was used for the data, a regression model was generated, the Cobb Douglas model was modified and solved using MathLab(2015) the output elasticities were generated and the modified Cobb Douglas model was also generated. The DO was found to be in the range of 12.78616mg/L to 17.28149mg/L for the treatment which has exceeded the maximum for any fish to survive.  Further an R² value of 71.39% was obtained which shows that the various components of the model were able to account for 71.39% of the variation in the given period of 11 weeks. A comparative analysis was done, the percentage variation of the DO_CD and DO_REG are <0.005 which gives good credence to the modified Cobb Douglas model