Applied Mathematics for Business and Economics

Lecture Note Differentiation

eRbIR)as;ral;éf¶. cUr):ansμannUv kMlaMgBlkmμbEnßmEdlKitCaem:agedIm,IbegáInplitpl

RbcaMéf¶kñúgkMrit12.5Ékta. (The daily output at a certain factory is (

QL)= 300 L^23

rce measured

t by

24

units, whereLdenotes the size of the labor fo in worker-hours.

Currently 512 worker-hours of labor are used each day. Estimate the number or

additional worker-hours of labor that will be needed to increase daily outpu

12.5 units.) (Answer: 0.5)

éføedImrbs;plitkrmñak;kMNt;edayGnuKmn_ ()^3

1

642 400

6

Cq=+ +q q

Ék kMritcrnþ¬Fm a¦énplitkmμesμInwg 4 Ékta. cUr)a:n;sμannUvbrimaN

plitEdlplitkrKYrkat;bnßy edIm,Ikat;bnßyéføedIm 130$. (A manufacturer’s total

cost is ()

enAeBlEdl

taRtUv)an μt

q

plit.

Cq=+ +^1 q^3642 q 400 dollars wh

6

en q roduced. The current

amount by which the manufacturer

total cost by $130.)

25

units are p

level of production is 4 units. Estimate the

should decrease production to reduce the

tamkMNt;Rta)anbBa¢ak;faxqñaMbnÞab;BIqñaM1988 Bn§elIkmμsiT§CamFüm eTAelIpÞHEdl

manbnÞb;bI enAkñúgshKmn_mYykMNt;edayTx( )=++ 60 x^32 40 1,

):an;sμannUvkMeNInBn§CaPaKrykñúgkMlugqmasTI1énqña 2.(Records indicate that

200 duløa.

M199

xyears after 1988, the average property tax on a three-bedroom home in a certain

community was ()

Tx=++ 60 x^3240 x1, 200dollars. Estimate the percentage by

which the property tax increased during the first half of 1992.)

(Answer: 6)

6 plitplenAkñúgeragcRkmYyKW QK( )= 400 K^12 Ékta Edl Ktag[mUlFnvinieyaK

rbs;Rkumh‘un. ):an;sμannUvkMeNInCaPaKryénplitpl EdlCalT§plénkarekIneLIg

1PaKryrbs;mUlFnvinieyaK. (The output at a certain fact ()

2

ory is QK= 400 12

units, whereKdenotes the firm’s capital investment. Estimate the percentage

ncrease in output that will result from a 1 percent increase in capital

investment.)(An

K

i

swer: 0.5 percent)

27 plitplecjBIeragcRkmYykMNt;edayGnuKmn_ = 600 K^123 Ékta EdlKtag[

mUlFnvinieyaK ehIyLtag[TMhMkMlaMgBlkmμ.cUr):an;sμankMeNInCaPaKryénplitpl

EdlekIteLIgedaysarkMeNIn2PaKryrbs;kMlaMgBlkmμebIvinieyaKmUl

ut a certain factor is

Q L^1

FnB bYl.

(The outp a y

Mu ERbR

t QKL= 600 12 13where Kdenotes the capital

investment and Lthe size of the labor force. Estimate the percentage increase in

output that will result from 2 percent increase in the size of the labor force if

capital investment is not changed.) (Answer: 0.67 percent)