Assignment Beni Ade Gunawan
Transcript of 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*