Lecture Note Function of Two Variables
change in output that will result if and additionalଵ
ଶhour of skilled labor is used
along with an additional 2 hours of unskilled labor. (Answer: 61.6)eragcRkmYyplit)an Qx Ékta kñúgmYyéf¶² EdlxKWCacMnYn
em:agEdleRbIR)as;kMlaMgBlkmμCMnaj nigyKWCacMnYnem:agEdleRbIR)as;kMlaMgBlkmμminCMnaj.
bc©úb,nñeKeRbIkMlaMgBlkmμCMnajcMnYn 80 em:ag nigkMlaMgBlkmμminCMnajcMnYn 200 em:agCaerogral;
éf¶. eRbIrUbmnþDIepr:g;Esülsrubrbs;GnuKmn_ QedIm,I):an;sμanBIbrimaNERbRbYlénplitpl Edl
ekItBIkareRbIR)as;bEnßmnUvkMlaMgBlkmμCMnajcMnYnknøHem:agnigkMlaMgBlkmμminCMnajcMnYn 2 em:ag.
(),y=++0.08x^22 0.12xy0.03y16 At a certain factory, the output is QKL= 120 12 13units, where K denotes the capital
investment measured in units of $1,000 and L the size of the labor force measured
in worker-hours. The current capital investment is $400,000 and 1,000 worker-
hours of labor are currently used. Use the total differential of Q to estimate the
change in output that will result if capital investment is increased by $500 and
labor is increased by 4 worker-hours.plitplecjBIeragcRkmYykMNt;edayGnuKmn_QK= 120 12 13LÉkta EdlKtag[vinieyaKmUl
Fn KitCaBan;duløa ehIyLKWCaTMhMkMlaMgBlkmμEdlKitCaem:agkmμkr.
bc©úb,nñeKeRbIviinieyaKmUlFncMnYn 400000 duløa nigkMlaMgBlkmμcMnYn 1000 em:agkmμkr. cUreRbI
DIepr:g;Esülsrubrbs;GnuKmn_QcUr):an;sμanbrimaNERbRbYlrbs;plitplEdlekIteLIgedaysar
eKbegáInvinieyaKmUlFncMnYn 500 duløa nigbegáInkMlaMgBlkmμcMnYn 4 em:agkmμkr.
17 A grocer’s daily profit from the sale of two brands of orange juice is ܲሺݕ,ݔሻൌ
ሺݔെ30ሻሺ70െ5ݔ4ݕሻሺݕെ40ሻሺ806ݔെ7ݕሻcents, where x is the price
per can of the first brand and y is the price per can of the second. Currently the
first brand sells for 50 cents per can and the second for 52 cents per can. Use the
total differential of P to estimate the change in the daily profit that will result if
the grocer raises the price of the first brand by 1 cent per can and raises the price
of the second brand by 2 cents per can. (Answer: 24 cents)
R)ak;cMeNjRbcaMéf¶rbs;Gñklk;eRKOgeTsmñak;BIkarlk;TwkRkUcBIrRbePTkMNt;edayGnuKmn_
ܲሺݕ,ݔሻൌሺݔെ30ሻሺ70െ5ݔ4ݕሻሺݕെ40ሻሺ806ݔെ7ݕሻesn EdlxCaéføkñúgmYykMb:ugén
TwkRkUcRbePTTI1 ehIyyKWCaéføkñúgmYykMb:ugénTwkRkUcRbePTTI2. bc©úbn,nñenHTwkRkUcRbePTTI1
lk;éfø 50 esnkñúgmYykMb:ug nigTwkRkUcRbePTTI2lk;éfø 52 esnkñúgmYykMb:ug. eRbIDIepr:g;Esül
srubrbs;GnuKn_PcUr):an;sμanbrimaNERbRbYlnUvR)ak;cMeNjRbcaMéf¶EdlekIteLIgedaysarGñklk;
begáInéføTwkRkUcTIRbePTTI1 cMnYn 1 esnkñúgmYykMb:ug nigbegáInéføTwkRkUcRbePTTI2cMnYn2esnkñúg
mYykMb:ug.
18 An editor estimates that if x thousand dollars is spent on development and y
thousand on promotion, approximately ܳሺݕ,ݔሻൌ20ݔଷଶ⁄ݕ copies of a new book
will be sold. Current plans call for the expenditure of $36,000 on development and
$25,000 on promotion. Use the total differential of Q to estimate the change in
sales that will result if the amount spent on development is increased by $500 and
the amount spent on promotion is decreased by $500.