Can I include a quotient as dependent variable and independent variables with same denominator in a linear model? How do we interpret such models?

I want to create a model in a food processing plant where my dependent variable is Electricity (KWhr) consumption per kg. Plant produce different food items with varying electricity consumption. I'm interested in knowing the impact of the proportion of each food item on consumption per kg. so my model is

 consumption per kg produced (Kwhr/kg) = alpha0 +alpha1(Food Item A/Total Production) + 
                                     alpha2(Food Item B/Total Production)+....+Other variables

Is it correct to frame the question like this?. I have Total Production on both sides of the equation as the denominator. What is the right way to approach this problem?. I would like to hear your thoughts on this. Any help is highly appreciated.

Topic linear-models data-science-model machine-learning-model data linear-regression

Category Data Science

1
answered at

Energy is additive but energy-per-kg is not.

Assume

$p_i$ be the energy consumption rate for food $i$ ($\mathrm{kJs^{-1}} = \mathrm{kW}$),

$t_i$ be the # second for producing 1 kg of food $i$ ($\mathrm{skg^{-1}}$)

$w_i$ be the amount of food $i$ produced ($\mathrm{kg}$)

so $p_it_iw_i$ will give us the total energy consumption for food $i$

Consequently,

$E = \sum_i p_it_iw_i + C $

$E$ is the total energy consumed, and $C$ encapsulate other energy consumption independent of the food.

For energy consumption per kg,

$E' = \frac{\sum_i p_it_iw_i + C}{\sum_i w_i} $

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