Lecture Note Function
consumers have been buying 3,000 lamps a month. The manufacturer wishes to
raise the price and estimates that for each $1 increase in the price, 1,000 fewer
lamps will be sold each month. The manufacturer can produce the lamps at a cost
of $4 per lamp. Express the manufacturer’s monthly profit as a function of the
price that the lamps are sold, draw the graph, and estimate the optimal selling
price.)(Answer: $6.50)19 eKRtUvP¢ab;ExSkabBIeragcRkGKÁisnIBImat;TenømçageTAeragcRkmYyEdlsßitenAeRtIymçageTotEdl
sßitenAeRkamExSTwkBIeragcRkGKÁisnIcm¶ay3000Em:RtehIyRbEvgTTwgrbs;TenøenaHKW900Em:Rt
. éføExSkabEdlP¢ab;qøgkat;TenøesμInwg 5duløa kñúgmYyEm:Rt rIÉéføExSkabEdlP¢ab;elIdIesμI nwg
4duløakñúgmYyEm:Rt. sUmemIlrUbbEnßm. cUrsresrtémøcMNayelIkartemøIgExSkabCaGnuKmn_
eTAnwgx. (A cable is to be run from a power plant on one side of a river 900
meters wide to a factory on the other side, 3,000 meters downstream. The cable
will be run in a straight line from the power plant to some point P on the opposite
bank and then along the bank to the factory. The cost of running the cable across
the water is $5 per meter, while the cost over land is $4 per meters. Let x be the
distance from P to the point directly across the river from the power plant and
express the cost of installing the cable as a function of x.)
(Answer: Cx() (=4 3, 000−+x)5 810, 000+x^2 )(^) Factory
Power Plant
x
900 m
(^3000) m
20 plitkreRKOgsgðarwmmñak;lk;tumYykñúgtémø 70duløa. éføedImsrubrYmmancMNayepSg²efr
8000 duløa nigéføedImplitkmμ 30duløacMeBaHtumYy.
k> etIKat;RtUvlk;tucMnYnb:unμanedIm,I[rYcedIm?
x>etIKat;RtUvlk;tucMnYnb:unμanedIm,I[)anR)ak;cMeNj 6000duløa?
K> ebIlk;dac; 150 tu etIKat;xatb:unμan nigcMeNjb:unμan?
X> enAelIRbB½n§G½kSEtmYy cUrsg;RkahVénGnuKmn_R)ak;cMNUl nigGnuKmn_éføedIm.
(A furniture manufacturer can sell dining-room tables for $70 apiece. The
manufacture‘s total cost consists of a fixed overhead of $8,000 plus production
costs of $30 per table.
a. How many tables must be the manufacturer sell to break even?
b. How many tables must the manufacturer sell to make a profit of $6,000?
c. What will the manufacturer’s profit or loss if 150 tables are sold?
d. On the same axes, graph the manufacture’s total revenue and total cost
functions.