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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
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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): Indirectheat rotary dryer: C = 1200 A”92 Directheat 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
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[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): (gm6.525 am): «0.2/79; 16/100): 4 /3/ ‘7 rcgﬁfﬂﬁ) : “0.0%0 go jd’ﬁg 310 XL;3§O
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+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
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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
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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
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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
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 Spring '07
 Gallivan

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