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Unformatted text preview: gLUTIOrUS MATH 122, SECTION 021 WORKSHEET 8
Show all work for full credit. 1. A model for the temperature, T (in °F), of a typical summer day is given by
T(t) = —0.60t2 + 7.875 + 72, Where t is time since 8AM. Find the maximumf the day. At What time is the temperature at its maximum? Prove your answer. MOW/W 7W “Owiﬁm +7.2 Max W:
Dame T (2): 4.2g + 2.8 714.5”): 13.500 (@952 Mushy
5mm! we 42248561 $172357: 2
“1%! fwd/16123718 ) 77W, g+ [0,5 t, H5,
#55 gngw/ 2. Find the quantity q that maximizes if the total revenue, R(q), and the
total cost, C(q), are given in;dollars by R01) = 350q8q2
C(q) = 1200+62q. What is the maximum proﬁt? Prove your answer. mm 7/2):/3502—X¢Z)—/I20o+5922) Max W:
77?): 3382, gZz/aOO 77/13):Z$8//8)‘8(/2§)1—J200
bent/ath 5'
0w K" 6mm; Vol/1+5 288vng :0 383—1102 3 _@ 2 ﬂ <W7T ’1? '/C0 ——n/ J 1 3/ W W“ 2 3. A local gym currently charges $38 / month and has a membership of 520 people.
Market research reveals that 24 fewer people would pay for a membership for each
$3 increase in dues, 24 more for each $3 decrease. What should the gym charge to maximize monthly How many people would pay for a membership at this
price? Prove your answer. H E*~_M_M~_ Cfnhml pom}? ’ 38 520 38(520) 54g,/44X : O
38+3X 520m /38*3X>{5ZO‘24X> Wx z {Ms
M MQXIMIZG )2 = /33*3X>/520 ‘2‘”) x = 4/5
59””th " 2/ ‘ @ﬂéﬂ/jy) + /5zo JIM/3) Chet/z: Mia? ZEél/X—ﬂ/l/x
2’: ‘9/Z—¥Zx+/5(90'7ZX @655 g) ’me/
12 : Ma” #ﬂ/X P: 38+ £4.53 t :5ZO'ZL/ﬂ/5) P: 5/‘ 5 11m... : FO I6
4. Your organization has decided to sell T—shirts to raise money. our supp ier charges a ﬁxed fee of $45. In addition, you pay $5.50 in production costs for each
shirt. Your price function is J p = 17.5 — 0.10q, where p is the price at which exactly q T~shirts will be sold. What price should you
charge to maximize How many T—shirts will you sell? Prove your answer. 6‘ 45+ 5502
E: 0254).:on P 2 my mama) Z: /ZS§«0.JOZZ P: Map/Shirt! WHWM MAX/M516 7: 0252 ’GJOgZ) " (gag/52') 77: Mi *0. )0; 7~ #5
D?ﬂbﬂfi’ltfli 7]“J :? @1795le PD/ﬂl'ﬁ" /2'0’2% SO [Max/2’02? : e/z Mmmmw’
m ’0“: r... a (go (9 Max /
2 a) Tsmaj ﬂ t T ...
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This note was uploaded on 02/21/2012 for the course MATH 122 taught by Professor Kustin during the Spring '08 term at South Carolina.
 Spring '08
 KUSTIN

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