Name: Y-o*'"
Honors PreCalculus
3.113.2 B Worksheet
Solve the following problems
1) TheJohnDeerecompanyhasfoundthattherevenuefromsalesoftractorsifafunctionofthepriceit
charges. lf the revenue
R
is
R(p)
: -! O' +1900p
2
a) What unit price p should be charge
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b) What
to maximize revenue?
&tie'
1c1L'v
Jo,r-tep--
R( rtct)
:
is
the maximum revenue?
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((Quu)
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(r,*rr, [, ,?;,*;,ri)
2) The price p and the quantity x sold of a certain product obey the demand equation
, = -!*+100 0<x<300
The revenue (R) =
,1 r*prJss the revenue as a function of
x R(x) =Q/z* rOc;\Y
What is the revenue if 100 units are sold?
b)
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J
irr,(r*)t
r.rr.u ( iur
)
What quantity maximizes revenue, and what
c)
pov.
is
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6,
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I
the maximum revenue?
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Y
vea-f*r = (rro,7,nir)
v o*|.,t
u{
vu*ta
d) What price should be charged to maximize revenue?rv--,
--,
3) David
has available 6000 meters of fencing and wants to enclose a rectangular plot using a river as one of the
borders. lfthefarmerdoesnotfencethesidealongtheriver,whatisthelargestareathatcanbeenclosed?
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Extra practice p, t92 #77
4) A projectile is fired at an inclination
of 45' to the horizontal, with a muzzlevelocity of 100 feet per
second.
The height h of the projectile is given by
h(x)
=:#+
(i00)'
x
where x is the horizontar distance from the firing point.
a) How far horizontally from the starting point is the height
of the projectile
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7c
b) what
is
:i
a maximum?
x(-,*. )
the maximum height of the projectite?
ht
l5(,-,x)
.. :?(159:ld^
'*--TwT-* | t>(1,>i -^6.";;
c) How far from the firing point wiil the projectire strike
the ground?
1
o > -}lx^
=ti( -U
rocvu x )- " ^'Lfu"-Jl'1-+-
-i)1,<
*fto*l
=ci
*l
-it*
fu,or'
'
* 9 t-.
d) Use your graphing calculator to graph this function
to verifu your resutts (draw a ,.orcL rk",.;
2.,4\
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t.
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otgr.pf)4:J&Zd'
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e) When the height of the projectile
how you found your answer.
'*
horizontally? Explain
'far-rn
Y -_b 2w; S t
et*rv,uJ y
is 50 feet above the ground, how far has it traveled
A \.= l-gu Qy
5o *
Y >?xs
€i" r,rk i,ttu.-1le..4-lrtu5
Challenge problem
j:l1l':l':-*:1", i:.i: the,shape ora rectangte with semicircres at each
ln" inside perimeter or
ll::l"ii:
thetrackistobe4o0meters. whatshouldthedimensionsof therectanglebesothattheareaofthe
"no.
--.-..
-\
rectangular part of the field is a maximum?
k
K
,.
/
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J.
t'lL - (/
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4=
rtru..>*\
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rrE iltJtuE
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If
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