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Rice price forecasting model

Incomplete work (continuing ) :
Rice has no primary substitute in southern India so it may not depend much on other groceries price.
Assume Rice is of only one grade for simplistic study of the case.
Let,
(r, theta, t)=spherical coordinates of a location with time 't' on spherical manifold(earth  surface)
P= Price of 1 Kg Rice at (r, theta, t)
R= Available rice at the location (r, theta, t)
Tcycle= Average total time for yielding rice from sowing to harvesting
D= Average daily intake of rice per capita


dP/dt=

dR/dt=

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