our submission should include (1) this document with your answers filled in, and (2) any/all\ additional files (.R files, .xlsx files, etc.) that you used to find your answers. You must work alone.\ This problem set explores a hypothetical regional market for fluid milk. For the purposes of this\ assignment, assume that because fluid milk is perishable and difficult to transport, all production and\ consumption of fluid milk must happen in the same region. In the region you are studying, there are fifty\ (n = 50) identical dairy farms that produce milk and one firm that processes the milk to sell to\ consumers. Every day, dairy farms buy grain (g, measured in kilograms) at price h (for this assignment,\ assume that h is equal to $1/kg) and feed it to their dairy cows to produce milk (m, measured in gallons)\ according to some milk production function f(g). They then sell their milk to the milk processor at the\ farmgate price p (measured in dollars per gallon, set by the processor). The milk processor buys all the\ milk produced from all the dairy farms in the region (M = n \\\\times m), processes it, and sells it to consumers\ for the retail price P (measured in dollars per gallon). The retail price is determined by the inverse\ demand function for milk: P = P(M). Both the individual dairy farms and the milk processor seek to\ maximize profit.