Lecture Note Function
(The price p and the quantity x sold of a certain product obey the demand
equation xp=−+ ≤≤ 5 100, 0 x 20
a. Express the revenue R as a function of x. (Remember,R=xp)
b. What is the revenue of the company if 15 units are sold?
c. Graph the revenue function.
d. What quantity x maximizes revenue? What is the maximum revenue?
e. What price should the company charge to maximize revenue?)
(Answer: a. R()xx=− + 51 2 20 x, b. $255 c. 500 d.x= 50 , $500 e. $10)11 ]sShkrmñak;Gacplitm:aej:kñúgtémø20duløakñúgmYyeRKOg. ebIeKlk;m:aej:kñúgtémøxduløakñúgmYy
eRKOg enaHGtifiCnnwgTij^120 −xeRKOgkñúgmYyEx. cUrsresrkenSamR)ak;cMeNjRbcaMExrbs;
]sSahkr CaGnuKmnnwgtémølk;. sg;RkahVrbs;GnuKmn rYctamry³enH cUr)a:n;sμanéfølk;Edl
RbesIrbMput. (A manufacturer can produce cassette tape recorders at a cost of $20
apiece. It is estimated that if the tape recorders are sold for xdollars a piece,
consumers will buy 120 −x of them a month. Express the manufacturer’s
monthly profit as a function of price, graph this function, and use the graph to
estimate the optimal selling price.)
(Answer: Px( )=−(x20 120)( −x), Optimal price: $70 per recorder)12 Write the equation for the line with the given properties
a. Through (2, 0)with slope 1.
b. Through (5, 2− )with slope
1
2
−
c. Through (2, 5)and parallel to the x axis
d.Though ()1, 0 and ()0,1
e. Through (2, 5)and ()1, 2
f. Through(1, 5)and (3, 5)
13 éføedImsrubrbs;]sSahkrN_mñak; rYmmancMNayepSg²Edlefr KW 5000duløabUknwgéføedImplit
kmμesμInwg 60 duløakñúgmYyÉkta. cUrsresrkenSaméføedImsrub CaGnuKmn_éncMnYnÉktaEdl)an
plitrYcsg;RkahV. (A manufacturer’s total cost consists of a fixed overhead of
$5,000 plus production costs of $60 per unit. Express the total cost as a function
of the number of units produced and draw the graph.). (Ans: yx=+ 60 5, 000)14 elakevC¢bNÐitmñak;manesovePAEpñkevC¢sa®sþEdlmantémø1500duløa EdlRtUv)ankat;rMelaH
efrrhUtdl;sUnükñúgry³eBldb;qñaM. mann½yfa témørbs;esovePATaMgenaHnwgFøak;cuHkñúgGRtaefr
rhUtdl; vaesμIsUnüenAcugRKaénry³eBldb;qñaM. cUrsresrkenSammYytag[témørbs;esovePA
CaGnuKmn_én eBl rYcsg;RkahV. (A doctor owns $1,500 worth of medical books
which, for tax purposes, are assumed to depreciate linearly to zero over a 10-
year period. That is, the value of the books decreases at a constant rate so that it
is equal to zero at the end of 10 years. Express the value of the books as a
function of time and draw the graph.)(Answer: yx=−+ 150 1, 500).