CK12 Calculus - Single Variable

We first note that sincethis is a real-lifeapplication,we observethat both quantities, and are
positiveor else the problemmakesno sense.Theseconditions,togetherwith the fact that the zero of
is locatedat suggestthat the actualdomainof this functionis This domain,which
we refer to as afeasibledomain, illustratesa commonfeatureof optimizationproblems:that the real-life
conditionsof the situationunderstudydictatethe domainvalues.Oncewe makethis observation,we can
use our First and SecondDerivativeTests and the methodfor findingabsolutemaximumsand minimums
on a closedinterval(in this problem, ), to see that the functionattainsan absolutemaximumat
at the point So, charginga priceof will resultin a total of tires being
sold.
In additionto the feasibledomainissueillustratedin the previousexample,manyoptimizationproblemsinvolve
otherissuessuchas informationfrom multiplesourcesthat we will needto addressin orderto solvethese
problems.The next sectionillustratesthis fact.
Primaryand SecondaryEquations
We will oftenhaveinformationfrom at leasttwo sourcesthat will requireus to makesometransformations
in orderto answerthe questionswe are facedwith.To illustratethis, let’s returnto our Lessonon Related
Ratesproblemsand recallthe right circularconevolumeproblem.