Assignment Beni Ade Gunawan

8/12/2019 Assignment Beni Ade Gunawan

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Assignment of Mathematics

Quiz

Yogi abdi prima

1110524014


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Question

1) If wehave the equation

a) 4x + 8y = 32

b) 5x - 6y = 30

hou!" #a$e the %u&ve f&o# the equation of above'

2) if we $now the equation is

Q = 340 ( 15

Q = 60 + *

-eteine whi%h one is the su,,!y equation an" why

-eteone the ,&i%e quantity at #a&$et equi!ib&iu# an" how #u%h the quantity

of ,&o"u%t at equi!ib&iu# !eve!

3) su,,ose that the %onsu#tion . invest#ent fun%tion a&e

/ = 4'200 + 085 y"

I = 600

a) eteine" the va!ue of in%o#e y) an" %onsu#,tion %) at

equi!ib&iu# !eve!'

b) If the inves#ent in%&ease be%o#e 800 what is the va!ue of in%o#e an"

%onsu#,tion a&e in%&ease how #any ,e&%entae the e%ono#i% &oss

an" #a&ina! ,&o,en%ity to save

4) if we have the / = + 5q + 250000

a) ow #u%h the quantity shou!" be ,&o"u%e in o&"e& to et #ini#u# %ost


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b) hat is the va&iab!e the va!ue of tota! %ostave&ae %ostva&iab!e %ostfix

%ost . #a&ina! %ost

5) a %o#,anie se!! 2 ,&o"u%t xy) the fun%tion f&o# the 2 ,&o"u%ts is 7

= 80'000x + 48000y ( - -

a) eteine how #u%h the quantity of . 9 shou!" be ,&o"u%e in o&"e&

to et &evenue #axi#a!''

b) hat is the va!ue of &evenue #axi#a!

6) shou!" you w&ite "eteinan 3 &ow . 3 %o!!u#n'':

he so!ution1)

a) he axist of equation xy = 0

4x + 8y = 32

4x = 32

= 8 80)


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he axist of equation to yx = 0

40) + 8y = 32

y = = 4 04)

b) he axist of equation to xy = 0

5x ( 60) = 30

5x = 30

= 6 60)

he axist of equation to yx = 0

50) ( 6y = 30

6y = -30

9 = -5 0-5)


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2)

a' Q = 340 ( 15,

b' Q = 60+*,

his equation is the su,,!y equation be%ause ,ositive s!o,e 60+*,) o& the

%oefi%ien is ,ositive

b) if the equi!ib&iu# %on"ition

Q"=Qs

340-15,=60+*,

340-60=*,+15,

280=24,

=1166;

Q=60+*1166;)

Q=1651

(3)

/ = 4200 + 085 y"

I = 600

a'

he va!ue of in%o#e at equi!ib&iu# !eve!

9 = / + I


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9 = 4200 + 085 y + 600

9 - 085 = 4800

015 y = 4800

9 = 32000

he va!ue of %onsu#,sion at equi!ib&iu# !eve!

9 = / + I

32000 = / + 600

/ = 32000 ( 600

=31400

b'

y = y1 - y0 y0 = 32000

y1 = / + I I

= 4200 + 085y + 600 + 200

015y = 4200 + 800

015y =5000

9=3333333

y = y1 - y0

=3333333 ( 32000

=133333 in%o#e in%&ease

/ = ''''

= 31400


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/1 = 4200 + 085 3333333)

= 4200 + 2833333

= 3253333

/ = /1 - /0

= 3253333 ( 31400

=113333 %onsu#,tion in%&ease

q = x 100= + 5 = 0

=

=

=40000

Q = 200

the va!ue of tota! %ost

/= +5Q+250000

= +5200)+250000

=1000+1000+250000

=252000

the va!ue of ave&ae %ost

?/=


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=

=1260

the va!ue of va&iab!e %ost

@/= +5Q

= +520)

=10000+100

=10100

the va!ue of fixe" %ost

A/= 250000

#a&ina! %ost

/=

=

=12600

5) =80000x + 48000y ( 4 - 8 -8xy

evenue #axi#u#>x=0 >y=0

>x=80000-8x-8y

>y=48000-16y-8x

80000-8x-8y


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48000-16y-8x -)

32000+8y = 0

8y=-32000

9=-4000

80000-8x= 8y

80000-8x = 8-4000)

80000-8x = -32000

-8x = -32000 ( 80000

-8x = -112000

= 14000

= 8000014000) + 48000- 4000) ( 4

= 464000000

6) fin"in the "eteinant of ? 3 &ow an" 3 %o!ou#'

2 8 0 2 8 B = 14+0+0)--504+o+o)

B = -* 1 1 -* 1 B = 518

0 0 ; 0 0

;) /=25000 + 40q + 0'005

=100q ( 0'01

a) ow #u%h the quantity shou!" be ,&o"u%e in o&"e& to et ,&ofit #axi#u#

b) hat is the va!ue of tota! %ost va&iab!e %ost fix %ost ave&ae %ost #a&ina! %ost an" tota! &evenue


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%) hat is the va!ue of ,&ofit #axi#u#

") ow stae fo& answe&in this ,&ob!e#

o!ution

Cn su,,ose that

?n" = 100q ( 0'01

a) /a!%u!ation of the quantity shou!" be ,&o"u%t in o&"e& to et the

#axi#u# ,&ofit7

#ax= (/

100q ( 0'01 ( 25000 + 40q + 0'005

60q ( 0'015 -25000

e have to "e&ive this equation to et the va!ue of q so we ot 9> =

60 ( 003q

Q= 2000

b) Dva!uation of the tota! %ost /

/=25000 + 40q + 0'005

/= 25000 + 402000) + 0005 )

/= 125000

Dva!uation of va&iab!e %ost @/


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@/= 40q + 0'005

@/ = 402000)+0'005 )

@/ = 100000

we have A/ f&o#e this fou! /=A/+@/)

so A/ = 25000

?/= = = 625

Dva!uation of #a&ina! %ost /

a&ina! %ost is the fi&st "evivation of tota! %ost so7

9= 40q + 0'005

9>=40+001q 40+0'012000)= 60

Dva!uation of tota! &evenue

= 100q-1'01 we have

he va!ue of q=2000 so7

= 160000

%) @a!ue of ,&ofit #axi#u#

#ax= (/

#ax=160000-125000=35000


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8) =150-1'5q

/=;50+15q+05

a#e question as exe&%i% nu#be& ;

o!ution

Ain"inthe va!ue of quantity

= xQ 150-15q)q

=150q-15

=-/

=150q-15 ) -;50+15q+05

=135-4q

o q= = 333;5

a) /=

/=;50+15q+05

/=;50+15333;5)+05

/= 180;5;

@/= 15q+05 15333;5)+05

@/ = 105;5;


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A/=;50

?/= = = 5415

/= /=;50+15q+05

a&ina! %ost is the fi&st "evivation of tota! %ost so7

o y>=15+q

/=15+333;5 = 483;5

= 150q-15

= 150333;5)-15

= 4*8*16

axi#u# ,&ofit=

#ax= (/

#ax = 4*8*16 - 180;5;

#ax = 31815*

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