Billy’s Box Company sells boxes with the following very particular restrictions on their dimensions.
1. The length, width, and height, in cm, must be all integers.
2. The ratio of the length to the width to the height must be 4:3:5.
3. The sum of the length, width, and height must be between 100 cm and 1000 cm, inclusive.
Stefan bought the box with the smallest possible volume, and Lali bought the box with the largest volume less than 4 m3.
Determine the dimensions of Stefan and Lali’s boxes.
There are 75 boxes that the company sells:
dimensions (cm) Volume (m^3)
36 27 45 0.04374
40 30 50 0.06000
44 33 55 0.07986
48 36 60 0.10368
52 39 65 0.13182
56 42 70 0.16464
60 45 75 0.20250
64 48 80 0.24576
68 51 85 0.29478
72 54 90 0.34992
76 57 95 0.41154
80 60 100 0.48000
84 63 105 0.55566
88 66 110 0.63888
92 69 115 0.73002
96 72 120 0.82944
100 75 125 0.93750
104 78 130 1.05456
108 81 135 1.18098
112 84 140 1.31712
116 87 145 1.46334
120 90 150 1.62000
124 93 155 1.78746
128 96 160 1.96608
132 99 165 2.15622
136 102 170 2.35824
140 105 175 2.57250
144 108 180 2.79936
148 111 185 3.03918
152 114 190 3.29232
156 117 195 3.55914
160 120 200 3.84000
164 123 205 4.13526
168 126 210 4.44528
172 129 215 4.77042
176 132 220 5.11104
180 135 225 5.46750
184 138 230 5.84016
188 141 235 6.22938
192 144 240 6.63552
196 147 245 7.05894
200 150 250 7.50000
204 153 255 7.95906
208 156 260 8.43648
212 159 265 8.93262
216 162 270 9.44784
220 165 275 9.98250
224 168 280 10.53696
228 171 285 11.11158
232 174 290 11.70672
236 177 295 12.32274
240 180 300 12.96000
244 183 305 13.61886
248 186 310 14.29968
252 189 315 15.00282
256 192 320 15.72864
260 195 325 16.47750
264 198 330 17.24976
268 201 335 18.04578
272 204 340 18.86592
276 207 345 19.71054
280 210 350 20.58000
284 213 355 21.47466
288 216 360 22.39488
292 219 365 23.34102
296 222 370 24.31344
300 225 375 25.31250
304 228 380 26.33856
308 231 385 27.39198
312 234 390 28.47312
316 237 395 29.58234
320 240 400 30.72000
324 243 405 31.88646
328 246 410 33.08208
332 249 415 34.30722
ct =
75
Stefan's box is 36 cm x 27 cm x 45 cm for a volume of 0.04374 cubic meters. Lali's is 160 cm x 120 cm x 200 cm for a volume of 3.84000 cubic meters.
clearvars,clc
unit=[4,3,5];
ct=0;
for mult=1:1000
box=mult*unit;
if sum(box)>1000
break
end
if sum(box)>=100
V=prod(box)/1000000;
fprintf('%4d %4d %4d %10.5f\n',box,V)
ct=ct+1;
end
end
ct
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Posted by Charlie
on 2024-01-28 10:33:05 |
computer solution
