Class

Meding

#19

-Let

c(x)and

R(x)

be

the

totar

cost

and

revenue

functions,

respectively.

-Then

theprofit

function

is

given

by,

n(x):

R(x)

_

C(x)

-T:.fo{

l(sales

quantiry)

formaximum

profit,

find

where

n,G):0.

S.ince

rc,(x):R,(x)

_

C,(*),

r

'(x) willoccur

where

R

,(x)

:

C

,(x).

Look

here

for

minimum

profit

also.

-R'(x):C

'(x)

is

where

marginal

revenue:

marginal

cost.

ffi*TR(x)

:5x

-

'003x2

and

c(x)

=

300

+

1.14

find

x

(number

of

units)

that

maximizes

profit

for

/ru/"t

c

T(x)

s

,?(x)-

Cftr)

s

9,?N

-,doty.\

7ao

77.?x)s

l,f

-

,aot% .=o

*

*=

6,fo

t"/il:

*,

oo

c

t(odo)

a

?aZ

f

IT(al

=

-.gao

fTftoaa)

s

Aao

<-

So,

)t

=e,fA

H-i

b?*in

*54.{4.,rfr*

-Note

thd

revenue

generated

equals

the

price

ofthe

item

sord

times

the

number

of

items

sord.

If

p:

the

price

of

each

item

ard

x

:

the

number

*iA,

irrJ

n1*;

:

p

".

-----

--

Example:

Let

x:rnrmber

ofpeople

attending

an

event

and

p:

70_

02x

be

the price

of

a

ticket.

As

the

number

attendingincreases'

the price

otttt*t,

?1

ur

th.

p;;;;r"ases,

the

numbei

attending

decreases

(makes

more

sense)'

Find

a)

the

tolal

t"t'"n"t,

R(^)

'b).the

*""oi;,

iflJoo

u,r*a,

,)

il;;;"dance

that

maximLes

revenue,

fl,5

Bffi:Tf:X*:ffi,

"r-,i"?;_;*;;;;:

;;rru

ii

til;;;;;,,

how

much

pront

do you

e)

fttxt=

Y'*=

(za-,o1'r.)t'x

s

?oX-,o47L

"e\

RtSaao):

3a.,ooo

e)

Rtx\r?o-,o')2.

so

-+

?1

sl?,fo

/)

ys

?o-.03(tz,fo)s3d

e)

Rttr{o)s

Lt,&fa

4)

?rr.t

Zua(

b74,-v&.

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