{VERSION 3 0 "IBM INTEL NT" "3.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 }{CSTYLE "" -1 256 "" 0 1 0 0 0 0 1 1 0 0 0 0 0 0 0 } {CSTYLE "" -1 257 "" 1 12 0 0 0 0 1 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 258 "" 1 12 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 259 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 260 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 261 "" 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 }{CSTYLE "" -1 262 "" 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 }{CSTYLE "" -1 263 "" 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 }{CSTYLE "" -1 264 "" 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 }{CSTYLE "" -1 265 "" 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 }{CSTYLE "" -1 266 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 267 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 268 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 269 "" 0 1 0 0 0 0 0 1 1 0 0 0 0 0 0 }{CSTYLE "" -1 270 "" 0 1 0 0 0 0 1 1 1 0 0 0 0 0 0 }{CSTYLE "" -1 271 "" 0 1 0 0 0 0 0 1 1 0 0 0 0 0 0 }{CSTYLE "" -1 272 "" 0 1 0 0 0 0 1 1 1 0 0 0 0 0 0 }{CSTYLE "" -1 273 "" 0 1 0 0 0 0 0 1 1 0 0 0 0 0 0 }{CSTYLE "" -1 274 "" 0 1 0 0 0 0 1 1 1 0 0 0 0 0 0 }{CSTYLE "" -1 275 "" 0 1 0 0 0 0 1 1 1 0 0 0 0 0 0 }{CSTYLE "" -1 276 "" 0 1 0 0 0 0 0 1 1 0 0 0 0 0 0 }{CSTYLE "" -1 277 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 278 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 279 "" 0 1 0 0 0 0 0 1 1 0 0 0 0 0 0 }{CSTYLE "" -1 280 "" 0 1 0 0 0 0 1 1 1 0 0 0 0 0 0 }{CSTYLE "" -1 281 "" 0 1 0 0 0 0 0 1 1 0 0 0 0 0 0 }{CSTYLE "" -1 282 "" 0 1 0 0 0 0 1 1 1 0 0 0 0 0 0 }{CSTYLE "" -1 283 "" 0 1 0 0 0 0 0 1 1 0 0 0 0 0 0 }{CSTYLE "" -1 284 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 285 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 286 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 287 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 288 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 289 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 290 "" 0 1 0 0 0 0 0 1 1 0 0 0 0 0 0 }{CSTYLE "" -1 291 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 292 "" 0 1 0 0 0 0 0 1 1 0 0 0 0 0 0 }{CSTYLE "" -1 293 "" 0 1 0 0 0 0 1 1 1 0 0 0 0 0 0 }{CSTYLE "" -1 294 "" 0 1 0 0 0 0 0 1 1 0 0 0 0 0 0 }{CSTYLE "" -1 295 "" 0 1 0 0 0 0 1 1 1 0 0 0 0 0 0 }{CSTYLE "" -1 296 "" 0 1 0 0 0 0 0 1 1 0 0 0 0 0 0 }{CSTYLE "" -1 297 "" 0 1 0 0 0 0 1 1 1 0 0 0 0 0 0 }{CSTYLE "" -1 298 "" 0 1 0 0 0 0 0 1 1 0 0 0 0 0 0 }{CSTYLE "" -1 299 "" 0 1 0 0 0 0 1 1 1 0 0 0 0 0 0 }{CSTYLE "" -1 300 "" 0 1 0 0 0 0 0 1 1 0 0 0 0 0 0 }{CSTYLE "" -1 301 "" 0 1 0 0 0 0 1 1 1 0 0 0 0 0 0 }{CSTYLE "" -1 302 "" 0 1 0 0 0 0 0 1 1 0 0 0 0 0 0 }{CSTYLE "" -1 303 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 304 "" 0 1 0 0 0 0 0 1 1 0 0 0 0 0 0 }{CSTYLE "" -1 305 "" 0 1 0 0 0 0 1 1 1 0 0 0 0 0 0 }{CSTYLE "" -1 306 "" 0 1 0 0 0 0 0 1 1 0 0 0 0 0 0 }{PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Heading 1" -1 3 1 {CSTYLE "" -1 -1 "Times" 1 18 0 0 0 1 2 1 2 2 2 2 1 1 1 }1 1 0 0 8 4 1 0 1 0 2 2 0 1 }} {SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT 259 10 "MATH-1850 " }{TEXT -1 1 " " }{TEXT 260 18 "COMPUTER PROBLEM 2" }{TEXT -1 54 " DUE: Tuesday, S eptember 12, 2000, in your lab class" }}{PARA 0 "" 0 "" {TEXT -1 17 " \nTeam members: " }{TEXT 266 54 "(All lines for answers below will e xtend as you type.)" }{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 0 "" 0 "" {TEXT -1 16 " (1) " }{TEXT 261 0 "" }{TEXT -1 0 "" }{TEXT 263 17 " SOLUTION " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 16 " (2) " }{TEXT 264 9 " \+ " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 16 " (3) " }{TEXT 262 0 "" }{TEXT -1 0 "" }{TEXT 265 9 " \+ " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 25 "Score: / 6\n" }}}{SECT 1 {PARA 3 "" 0 "" {TEXT 258 13 " INSTRUCTIONS " }{TEXT 257 20 "(Click box in front)" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 1192 "It is strongly s uggested that this project be worked in teams (of up to 3 persons). A pproaches may be discussed among different teams, but each team must w rite their OWN report.\nREQUIREMENTS OF REPORT:\n- Mathematical conten ts (correctness and completeness) counts most. Solve the problems and \+ show all essential calculations (commands and output) and plots. Pleas e do not submit work that is not essential (e.g. checking out how the \+ function fplot in Problem 1 works - this may be essential to your unde rstanding, but it s not essential for the reader).\n- Explain the step s you carry out. Explain the approaches/techniques that you use.\n- Ad d explanations and answer questions where asked to do so. By all means , include additional explanations/observations/conclusions that come t o your mind! (This could translate to extra credit.)\nHOW TO SUBMIT TH E REPORT\nEach team submits ONE printed copy (stapled) by the due date . (Please save the electronic version, as you will be asked to submit \+ that, too, at a future time.)\nYou can print from inside your Maple wo rksheet (choose File/Print or click on the printer button). Set the ZO OM FACTOR to 100% (smallest magnifying glass) before printing.\n" } {TEXT 256 62 "Please remove these instructions before submitting the r eport." }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart:" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 276 "A farmer wishes to fence a rectan gular pasture with a total area of 1000 square yard, and he wants to d ivide it into two parts with a fence across the middle. Fencing aroun d the outside costs $5.00 per yard, but he can use less expensive fenc e at $2.00 per yard as a divider." }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 72 "(a) Express the cost of this encl osure as a function of one variable. " }{TEXT 267 138 "(Write your fu nction on the provided answer line below. However, attach a diagram o f the enclosure and your work to obtain the function.)" }{TEXT -1 0 " " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 6 " \+ " }{TEXT 268 19 "Answer to Part (a) " }{TEXT 269 9 " C = 10" }{TEXT 270 1 "x" }{TEXT 271 9 " + 12000/" }{TEXT 274 4 "x , " }{TEXT 279 6 "w here " }{TEXT 280 1 "x" }{TEXT 281 51 " = the length of the rectangula r region OR C = 12" }{TEXT 272 1 "x" }{TEXT 273 9 " + 10000/" } {TEXT 275 1 "x" }{TEXT 276 9 " , where " }{TEXT 282 1 "x" }{TEXT 283 40 " = the width of the rectangular region " }{TEXT -1 4 " " }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 4 " " } {TEXT 277 24 " NOTE: The function C " }{TEXT 256 2 "= " }{TEXT 278 2 "10" }{TEXT 257 1 "x" }{TEXT 258 9 " + 12000/" }{TEXT 259 58 "x will be used in order to answer the following questions." }{TEXT -1 0 "" } }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 70 " (b) Define the function in Part (a) as a function using Maple syntax. " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "C := x -> 10*x + 12000/x;" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 5 "C(x);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 0 "" 0 "" {TEXT -1 37 "(c) Graph your function in Part (b)." }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "plot(C(x),x);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 11 "(d) Since " }{TEXT 284 1 "x" }{TEXT -1 22 " is a dimension, then " }{TEXT 285 1 "x" }{TEXT -1 45 " > 0. Plot the gr aph for positive values of " }{TEXT 286 1 "x" }{TEXT -1 68 " which wil l show the decreasing and increasing natural of the graph." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "plo t(C(x),x=0..100);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 " " 0 "" {TEXT -1 225 "(e) Your graph in Part (d) above has a local min imum point where the graph of the function changes from decreasing to \+ increasing. Obtain a graph of the function which better shows the loc al minimum point by restricting the " }{TEXT 287 1 "x" }{TEXT -1 8 " a nd/or " }{TEXT 288 1 "y" }{TEXT -1 8 " values." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "plot(C(x), \+ x=34..35);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 135 "(f) Using your graph in Part (e) above, find the approx imate dimensions of the rectangular region which will result in the le ast cost." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT 289 33 " Ans wer to Part (f) Length " }{TEXT 290 61 " The length is approximatel y 34.64 yards obtained from the " }{TEXT 293 1 "x" }{TEXT 294 41 "-coo rdinate of the local minimum point " }}{PARA 0 "" 0 "" {TEXT -1 0 " " }}{PARA 0 "" 0 "" {TEXT -1 33 " " } {TEXT 291 12 " Width " }{TEXT 292 79 " The width is approximat ely 28.87 yards obtained from the equation y = 1000/" }{TEXT 295 1 "x " }{TEXT 296 8 ", where " }{TEXT 297 1 "y" }{TEXT 298 46 " = the width of the rectangular region. Thus, " }{TEXT 299 1 "y" }{TEXT 300 8 " = \+ 1000/" }{TEXT 301 1 "x" }{TEXT 302 17 " = 1000/34.64 " }{TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 124 "(g) Using your graph in Part (e) above, find the approximate cos t of fencing for the rectangular region in Part (f) above.\n" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" } {TEXT 303 25 " Answer to Part (g) " }{TEXT 304 56 " The cost i s approximately $692.82 obtained from the " }{TEXT 305 1 "y" }{TEXT 306 43 "-coordinate of the local minimum point. " }}}}{MARK "2 0 0 " 8 }{VIEWOPTS 1 1 0 1 1 1803 }