Applied Mathematics for Business and Economics

Lecture Note Differentiation

9³00 nig 9³15? (An efficiency study of the morning shift at a certain factory

indicates that an average worker who arrives on the job at 8:00 A.M. will have

assembled f(xxx x)=− + +^32615 radios x hours later. Approximately how man

radios with the worker assemble between 9:00 and 9:15 A

enAkñúgeragcRkmYy plitplRbcaMéf¶esμInwg

y

.M? )

20 Qk( )= 600 k^12 Ékta Edlktag[vinieyaK

mUlFn KitCaÉkta1000duløa. vinieyaKmUlFncrnþ esμInwg 900000duløa. cUr):an;sμan

FnbEnßm cMnYn800duløa nwgmaneTAelIplitplRbcaMéf¶.

a certain factory, the daily output is

GMBI\T§iBlEdlvinieyaKmUl (At

Qk( )= 600 k^12 units, where k denotes the

itional capital i

21

capital investment measured in units of $ 1,000. The current capital investment is

$900,000. Estimate the effect that an add nvestment of $800 will

have on the daily output.) (Answer: 8 units)

enAkñúgeragcRkmYy plitplRbcaMéf¶KWQL( )=60, 000L^13 Ékta EdlLtag[TMhM

kMlaMgBlkmμ KitCaem:agkmμkr. fμI²enH MnYn1000em:agkmμkr

RtUv)aneRbIR)as;Caerograléf¶. cUr):an;sμan BI\T§iBleTAelIplitkmμEdlekIteLIg

ebIkMlaMgBlkmμRtUvkat;bnßymkenA 940em:agkm

kMlaMgBlkmμc

μkr> (At a certain factory, the daily

output is QL()=60, 000L^13 units, w

measured in worker-hours. Currently 1000 worker-hours of labor are use each

day. Estimate the effect on output that will be produced if the labor forc

940 worker-hours.)

enAkñúgeragcRkmYy plitplRbcaMéf¶kMNt;edayGnuKmn_

here L denotes the size of the labor force

e is cut to

22 QKL=3, 000 12 13Ékta

ktag[vinieyaKmUlFnrbs;Rkumh‘unEdlKitCaÉkta1000duløa ehIyLtag[TMhM

kMlaMgBlkmμKitCaem:agkmμkr. ]bmafavinieyaKmUlFncrnþKW400000duløa ehIyfa

kMlaMgBlkmμcMnYn 1331 em:agkmμkr RtUv)aneRbIR)as;ral;éf¶. cUreRbIkarviPaKm:aCINl

Edl

edIm,I):an;sμanGMBI\T§iBlEdl vinieyaKmUlFnbEnßm1000duløa niwgman lIplitpl

RbcaMéf¶ ebITMhMkMlaMBlkmμBMupøas;bþÚr. (At a certain factory, the daily output is

eTAe

QKL=3, 000 12 13where K denotes the firm’s capital investment measured in

units of $1,000 and L denotes the size of the labor force measured in worker-

hours. Suppose that the current capital investment is $400,000 and that 1,331

worker-hours of labor are used each day. Use marginal analysis to estimate the

effect that an additional capital investment of $1,000 will have on the daily

output if the size of the labor force i

AkñúgeragcRkmYykMNt;eday

s not changed. )( Answer: 825).

23 plitplRbcaMéf¶en QL( )= 300 L^23 Ékta EdlLtag[

kMlaMgBlkmμEdlKitCaem:agkmμkr. bc©úb,nñenH kMlaMgBlkmμ512em:agRtUv)an

TMhM