Lecture Note Function
(Answer: a.Cqt⎡⎤⎣⎦()=++ 625 t^225 t 900 b. $6,600 c.After 4 hours)
8 enAkñúgesdæviTüa R)ak;cMNUlRtUv)ankMNt;faCaTwkR)ak;Edl)anBIkarlk;plitpl ehIyesμIeTAnwg
plKuNrvagéfølk; pkñúgmYyÉkta nig cMnYnxÉktaénplitplEdl)anlk;. mann½yfa
R=xp. RkwtüRkmtRmUvkar Ecgfa pnig xTak;TgKña. ebImYyekIneLIg enaHmYyeTotRtUvfy
cuH. ]bmafa pnig xTak;TgKñatamry³ smIkartRmUvkar px=−+ ≤≤ 101 20, 0 x 200.
cUrsresrkenSamR)ak;cMNUlRCaGnuKmn_énx. (In economics, revenue R is defined as
the amount of money derived from the sale of a product and is equal to the unit
selling price p of the product times the number x of units actually sold. That is,
R=xp. I
wing
n economics, the Law of Demand states that p and x are related: As one
increases, the other decrease. Suppose that p and x are related by the follo
demand equation:px=− + 101 the revenue R as a function
of the number x of units sold.) (Answer:
20 , 0≤x≤ 200. Express
R(x)=− 110 xx^2 + 20 )
9 éfø pnigbrimaN xénplitplmYyEdl)anlk; eKarBeTAtamsmIkartRmUvkar
1
100, 0 600
6
px=− + ≤ ≤x.
k> sresrkenSamR)ak;cMNUlCaGnuKmn_eTAnwg x
x> ebIeKlk;plitplGs;200Ékta etIR)ak;cMNUlesIμb:unμan?
K> sg;RkahVrbs;GnuKmn_enH.
X> etIxesμIb:unμanEdlnaM[R)ak;cMNUlGtibrma? etItémøGtibrmaenaHesμIb:unμan?
g> rktémølk;EdlRkumh‘unRtUvkMNt; edIm,I[R)ak;cMNUlGtibrma.
(The price p and the quantity x sold of a certain product obey the demand equation
1
100, 0 600
6
px=− + ≤ ≤x
a. Express the revenue R as a function of x. (Remember,R=xp)
b. What is the revenue of the company if 200 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?)
(Ans: a.R()xx=− + 61 2 100 x, b.$13,333.33, c. 15,000 d.x= 300 , $15,000 e. $50)
10 éfø pnigbrimaN xénplitplmYyEdl)anlk; eKarBeTAtamsmIkartRmUvkar
xp=− +5100,0≤ ≤p 20.
k> sresrkenSamR)ak;cMNUlCaGnuKmn_eTAnwg x
x> ebIeKlk;plitplGs;15Ékta etIR)ak;cMNUlesIμb:unμan?
K> sg;RkahVrbs;GnuKmn_enH.
X> etIxesμIb:unμanEdlnaM[R)ak;cMNUlGtibrma? etItémøGtibrmaenaHesμIb:unμan?
g> rktémølk;EdlRkumh‘unRtUvkMNt; edIm,I[R)ak;cMNUlGtibrma.