A factory’s daily adjustment cost (in rupees) for producing units beyond a target of…

MATHEMATICS · Subjective · AoPS · Mathematics · Special Functions · Special Functions

Problem

A factory’s daily adjustment cost (in rupees) for producing

n

units beyond a target of

100

units is given by

C(n)=|n-100| + 0.01(n-100)^2 + 2500,

where

0\le n\le 200

. Determine the value of

n

that minimises this cost.