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practiceExam2s1solutions

practiceExam2s1solutions - Exam 2 Practice Exam Sl...

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Unformatted text preview: Exam 2, Practice Exam Sl Supplementary Information You may find some of the information on this page helpfiil in solving problems on the exam. Chemical En - ineerin ' Plant Cost Index M - A o8 No ob.) 4s 4:8 ho ~45 Marshall & Swi ! E v uitmem Cost Index 2004 2005 The Taylor series for y = y(x) is ‘° 1d”y +Ax= -— y(xo ) Enldx" (1536)" ’0 Problem 1: [10 points] You are designing a drying process for production of a pharmaceutical intermediate. Two types of dryers have been recommended with the following cost estimates (based on a CE index of 394): Indirect-heat rotary dryer: C = 1200 A”92 Direct-heat rotary dryer: C = exp[ 10.158 + 0.1003 In A + 0.04303 (1n A)2] In both cases, A is an area in fiz. Which dryer would be preferred for a process requiring 250 ft2 of drying area? If the process was later expanded by an additional 750 ft2 of drying area, which (1 er would ou use for the ex ansion. ”L Mira; E3 lwopfis‘zj)” : fi/W, 530 End" (,5 (ax/9 [/0/7‘5 riflOJ/é/Zs‘fl)r .fli‘MBKZmej 7, m) m )3? 11M 3%,” fl’3257j Wye/(L (3 /?00 (0/000) "(’13 fé 7&530 [7% bars? c w 3M») rmgazmm Q j 347/ 1g Ma” 16/ £290 5/4 Problem 2. [15 points] The heat capacity of a packing material being considered for use in a large reactor is given by CP(T)= 0.132 +1.56x10“T+2.64x 10‘ r2 +0.54ln(T) where the heat capacity is measured in cal/(g K) and T is the temperature in K. This means that 9.800) = 3.2826 and cP(500) : 3.6319. As part ofa design calculation, you need to know the temperature at which c, e 3. 5. (a) Use two steps of the bisection method to estimate the desired temperature. (b) Use two steps of the Newton- ~Raphson method starting from T= 500 to estimate the desired temperature. Ge) 15(2): (gm-6.525 am): «0.2/79; 16/100): 4 /3/ ‘7 rcgfifflfi) : “0.0%0 go jd’fig 310 XL;3§O {’CLf70) 3‘ (90H7 go gafjrfl “37511—75795 (é) 1/412: >01 no eff—’32? MW! we Ff—b‘) 5003-500 >6 : __ (t;(7€a)_3r§\ ‘ 0 {Wanna/fly? JV? 1:. 620 ... (go/5’ ((23) 35‘ =71>_ 252 ’ tea/04am“; —06075 3 [4aoj‘fsqg- esMc-L 3(425— g £64) 40(7) )5, [(2): [W +S:Z{x/0 Mr?” .530 M (Mex/04’ 5‘ ZXKW7/WME5— ‘5 5; = ;50057 073: L112 0667 F‘Cr 4:11“? 5.0132145; 1/0 [wt/2m W}; m) +5. WAMZWfl— —7 {6770 r5“. Mir/0 7/1/2119) k 0- 7* +12 056 7 " LHZCEP (44243) 05‘5” L Problem 2 (cont) Problem 3: [10 points] You are managing a small business that uses a small SUV for day to day operations. You anticipate that you will need to replace the SUV 1n 5 years at a cost of $25, 000. You are able to safely invest funds with your bank at an annual interest rate of 5% (a) One way to save the required money is to save a fixed amount every month for the next five years. How much will you need to save every month in order to have $25,000 in five years time? (b) Another way to save the required money would be to set aside a single lump sum now and let it accumulate interest for 5 years. What amount would you need to set aside 1n order to have $25 000 1n five years time. 44; p Wig: lama/”aw @ Wang: W 52 4$wme ”brief”?! 5/17% WW : am‘fmfi/Jc «mow/MW 7143650? c; 4/ F _, 25—000 1:: y 4:; 3; 2: (not; . “mg/‘04 :t‘aw b L: “T533 flex/Mfg ID (MW/M Partial“ Mia/Mata? fl2§flm [A W //\ f {a ‘44“ I“ M” WWW, wt/Mfwlt War/134543 /?/MA’$M4 Fifi/#12) "‘77 fl’ai)" )0 73:2 W7“ 47/50 or. in mm WMwa/é .- P %% [M m Problem 6: [15 points] In this problem, 6you aim to find a maximum of the function f (x y): 6—cos(x+ y)— sin(x)— cos(y). (a) Calculate the search direction for the first step of the steepest ascent method using the Origin, x: y: 0, as the starting point. Draw a sketch of the x y plane indicating the starting point and the search direction. (b) State (be defining a mathematical function) the one dimensional maximization problem that is defined by the first step of the steepest ascent method. (c) An alternative solution strategy is to use the univariate search method. If we hold y = constant in the first step of the univariate search, we seek to maximize the function f (x O): 5— cos(x)— sin(x) Use two iterations of the Newton- -Raphson method to estimate the value of x that maximizes this nction. FFFFF 3] L231 EFF/FF Fifi] %[ 1 50 gel/4%” )U‘Lr‘a *X/é‘rméon m( 364565) ._. 0 (F) 37%: Mgmw W ngj age, %[7C.0+0.M: Hal—M2 mien; & v‘i 4/6 461% (new W :37 61517 3530 :5 {[25 -/f 3.9) ‘“ 15H 0) f0 POW fmé/em 25 150,30) 5 (Os/Fl) Wed” (05(0) 2 6mm ~ ”7%) / Pr oble em 6 (cont ) wk K be» ' - fl W -fi) _, 5/7/0565)“7f4 (X) 7C5», /XL (66-) ; 2C5 5-K)»: (2:) «'Cwét) UYMMWK L70 We Wg waM ,,, 4/) —' [m-s: —— f[,/‘/__ %,?0' {/05 My? .__ J rsW~zos/a) " M f” I 0 _ 5—.— (osfl)"$trn (/)3 __ 761/ / flew) ’CO?/() 6325/? “gm Problem 1: [10 points] Five measurements are taken of the octane rating for a blend of gasoline. The results (in %) are 87.0, 86.0, 86.5, 88.0, 85.3. (a) State the sample mean for these measurements. _,._ I ”K, : JgflwswaésvsflS/sfiij b (b) State the sample standard deviation for these measurements. (XL 32): 36W -—.S?‘)”-06)/'4L{/”/'Z€3 S at?! 35753 i[w HZ Wan/W WK] 62/5323}: ”45 :7 g: £028 (c) Find a 99% confidence interval for the mean octane rating of this gasoline blend. fl 52+ arts/V “4,4,5 53/028 :Is’ deaf/“-f’fifl/ its! 17‘ “LL/(0‘75 7) Li; )(1070 Me‘s/4%}: [ 0:}? ) :ggrg‘é 3: 2/52? Problem 5: [10 points] You have purchased a machine that fills bags with candy. Each bag is supposed to weigh 16 02. A random sample of 6 bags gives the following weights (in 02.): 15.87, 16.02, 15.78, 15.83, 15.69, 15.81. You wish to test the hypothesis that the machine is working correctly by giving a mean fill weight of 16 02. Using the sampled data, do you accept or reject this hypothesis based on a 95% confidence level? 56‘: fl 21/6 ”‘ 2 6 N /5‘-57 H602 1L (975+ I)". X?+/;.(?+/5‘.¢/ __ macs é “W In? N 1, C20: *5“) '1 501/ 4772*)?! gems—.02} 521/;va _ @z’fi 2- ,olrzt/F’rnés’zwzt-"’z*‘oaL 0.0120 E! j 3” ...
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