I have one year sales data of a retail company and lets say I am forecasting the next month sales for the product. I have got the sales using time series in R. Now I want to forecast the price as well. I want to build a model using both the demand and price. My function should be f(DP) where D is demand and P is price. I want to maximize Revenue or Profit where Revenue=DP.
As of now, I forecasted sales and did a linear programming on Price itself to get optimal price of a single product. I want my model to be robust but this is chicken - egg theory where demand forecast is dependent on the price and price is dependent on demand. Please help by sharing some theories which would better fit for this or some R models.