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Hi I have similar problem here. I am trying to maximize sales to find an optimum price. I have fit a linear regression assuming a linear relation ship between price and quantity and other variables (Including Dummy variablles) impacting quantity. I am taking the regression function as an objective function which includes price as Independent and quantity as dependent.My prroblem is in lp solver my objective function becomes a linear regression equation (y(Quantity)=-0.02x (Price) + Constant (Constant after taking the scenario and intercept).

Can you help me how can I optimize above type of function ?

I have been struggling to identify the point of change in price which maximizes quantity.I have tried manually putting Drops and Ups in price and arrived at overall impact but I want to avoid manual intervention here and therefore thinking if lp solver would help me.

Thanks, Avani

Avani Shah
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Usually one first writes down a mathematical model, and then decide how to solve it. Not sure what you want, but an optimization model for the producer could look like:

 max profit = p*q - c*q
 q = -0.02 p + constant 
 p, q >= 0

where c is the unit cost. p and q are price and quantity. This is a quadratic model (p*q) so you need something more powerful than an LP solver. (Although for this small example you can do it by hand). There are of course many other models possible.

Erwin Kalvelagen
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