Optimization Problems

Transcription

1 -1-0 Y2K0U1g37 ok3uutxa1 YSDojfKtzwBagr0eb klflsch.w a yatlulu nr8iugzhkt0se ZrWe9s7eYrwv6ewdu.W J hmeaddfet ZwBijt7h9 RIAnNfoi3n5iFtOea JCuaMlXchuPl7uXs7.G Worksheet by Kuta Software LLC College Calculus (Conway) Optimization Problems d 9260D1S3S VKfu5tmaa uskoaf3ttwfayr3eq VLGLgCf.v v oasl4lq FrLi1gihXtAs0 arzewsje9rtveejdz.r Solve each optimization problem. Name 1) A supermarket employee wants to construct an open-top box from a by in piece of cardboard. To do this, the employee plans to cut out squares of equal size from the four corners so the four sides can be bent upwards. What size should the squares be in order to create a box with the largest possible volume? in Date in

2 -2-2 Q2g0k143Y wkuustyay VSeobfJtDwHaRrGe3 RLgL5C0.h u NAWl5l2 WriiHgNhStFsp drzeas1eerzvleodz.m e 3MzaVdHeg swbimtjho siinjf4iinniqtnea oc9a4lucvutlmulsf.5 Worksheet by Kuta Software LLC 2) A cryptography expert is deciphering a computer code. To do this, the expert needs to minimize the product of a positive rational number and a negative rational number, given that the positive number is exactly greater than the negative number. What final product is the expert looking for? No illustration necessary for this problem

3 -3-4 G2n0E1o3W EK0u4tbam NSNoxfhttwfa5rYem 3LuLMC1.5 1 rallilh mrriigihhtzsw 3rhefsKePrBvzevdo.a G HMnaFdme5 1wciEtWh6 li5n4fmitn1iltyew gchailuc8uiltuast.a Worksheet by Kuta Software LLC 3) A farmer wants to construct a rectangular pigpen using ft of fencing. The pen will be built next to an existing stone wall, so only three sides of fencing need to be constructed to enclose the pen. What dimensions should the farmer use to construct the pen with the largest possible area?

4 -4- B J260C113N YKpuqtYa9 0SnotfStawbawrme1 GLzLnC6.8 S IAVlwlc grmibgghytqsw vrzeoslerr2vhexdo.f M JM4aUdUeY EwtiVtNhy 2IRnufziVn1iGt3eb BCYaElkcxu8lvuRsE.T Worksheet by Kuta Software LLC 4) A rancher wants to construct two identical rectangular corrals using ft of fencing. The rancher decides to build them adjacent to each other, so they share fencing on one side. What dimensions should the rancher use to construct each corral so that together, they will enclose the largest possible area?

5 -5- E w230b193c okru0tpap TSjoyfgtVw6aPrwes rlfljcz.v b KAAl1ly ErNiugghxtOsT nroeps9eurqvneydi.u 0 VM2axdOeg 6wnimteho qifnrfzixnhiftae7 eclavl3cmumleu9sn.c Worksheet by Kuta Software LLC 5) A company has started selling a new type of smartphone at the price of $ x where x is the number of smartphones manufactured per day. The parts for each smartphone cost $ and the labor and overhead for running the plant cost $ per day. How many smartphones should the company manufacture and sell per day to maximize profit? No illustration necessary for this problem

6 -6- U h2x011w3f ykmuzthar JS4ovfxtEw6aTrDed al9lvca.n 9 TAKlflm TraiYgZhzt4sz DrIeCs6eRrovUeYdL.a B bmraedxeu kweiwtzh3 ni7nvfji2nqictmem 1CDaBlfcqu7lAursW.B Worksheet by Kuta Software LLC 6) Engineers are designing a box-shaped aquarium with a square bottom and an open top. The aquarium must hold ft³ of water. What dimensions should they use to create an acceptable aquarium with the least amount of glass? x x

7 -7- o H2d0s1g3Y vklugtyap OSNokf3tYwCaUrTeP 1L0LBC6.t S FAAlLl1 lraiug1hvtdsa PrIeKssearuvle5dO.X Y PM4aAdAeg iwki8tthb giqnlfnirnriztqeq 5Coa4lIcCuKlau7sg.J Worksheet by Kuta Software LLC 7) A geometry student wants to draw a rectangle inscribed in the ellipse x y. What is the area of the largest rectangle that the student can draw? y Example rectangle not optimal x

8 -8-0 V2D0k1q3s 6KEuitVa3 XSyoEfftvwsa0rYeN eltljcq.b o javlilr 4rciEgShTtrsE yrtevsbeqrpveefdm.4 v LMxagd9ex cwci4tphp wifnefsinnyi4txeu TChallMciuLl8uZsi.g Worksheet by Kuta Software LLC 8) Which points on the graph of yx are closest to the point (, )? y x

9 L0B1u3G FKWuAtyaQ 4SboyfvtowCaUrAea BLvLICH.q v zaslble FrZiDgmhStpsc WroevscefrUvceTdv.T 8 4MiaFdTeZ fwqiatih8 BIXnEfNiTnGiPt8e0 GCfarlLcyu5lMu4s4.v Worksheet by Kuta Software LLC 9) A geometry student wants to draw a rectangle inscribed in a semicircle of radius. If one side must be on the semicircle's diameter, what is the area of the largest rectangle that the student can draw? y Example rectangle not optimal x

10 -10- C b200b1l3h QK6uTtnar 4SBoef0tmwyaurleI 0L0LxCW.i 5 MAmlulK WreiRg3h1trsS 7r7eDsnelrEvkeLdX.9 4 3MoaSdNe0 nweiutnh3 ci4ngf3ihn4irt9eq SCaawlsc5uRlWulsD.q Worksheet by Kuta Software LLC 10) A graphic designer is asked to create a movie poster with a in² photo surrounded by a in border at the top and bottom and a in border on each side. What overall dimensions for the poster should the designer choose to use the least amount of paper? in in in in

11 -11- s v2v0b1p3v 9K6uetfaw tsnoafmtmwbalrkeb tllljcv.n D eaelkl3 Eroi2gShNtFsJ xrnemskebrpv1efdi.j 4 1MmajdbeV cwoimtnhv zi1nbfbisnsibtyep UCsa3lQcsuBlluYsl.P Worksheet by Kuta Software LLC 11) Which point on the graph of y x is closest to the point (, )? y x

12 -12-9 C2C0y1n3w dkmumtqa4 0S3oTfwt4wFaKrzef WLrLcC5.F m saylelo 6rMivgTh6trs6 qrgeesfesr9vreldf.c B HM9aBdEe2 Owaistnhr 6IVnUf7i5nMiwtPea rcmaqlxcpulljuaso.l Worksheet by Kuta Software LLC 12) Two vertical poles, one ft high and the other ft high, stand feet apart on a flat field. A worker wants to support both poles by running rope from the ground to the top of each post. If the worker wants to stake both ropes in the ground at the same point, where should the stake be placed to use the least amount of rope? ft ft ft

13 -13- W I2q021m35 IKnuot3an wsiobfttzwiakrrec BLULwCN.R T xallela drfizgwhttks5 2rUe7soenrWvMeldo.e f VMxatdkeU iwdixtjhr IItnBfRiEnrivtZec 3C1aslRcYuNliufs7.r Worksheet by Kuta Software LLC 13) An architect is designing a composite window by attaching a semicircular window on top of a rectangular window, so the diameter of the top window is equal to and aligned with the width of the bottom window. If the architect wants the perimeter of the composite window to be ft, what dimensions should the bottom window be in order to create the composite window with the largest area?