Applied Mathematics for Business and Economics

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.