## (Solved) A company assembles two products: A and B. Product A sells for \$1100/unit, and product B sells for \$2300/unit. A unit of product A requires 2 hours...

A company assembles two products: A and B. Product A sells for \$1100/unit, and product B sells for

\$2300/unit. A unit of product A requires 2 hours on assembly line 1 and 1 unit of raw material. A unit of

product B requires 2 units of raw material, 1 unit of A, and 2 hours on line 2. A unit of raw material may be bought

(for \$500/unit) or produced (at no cost) by using 2 hours of time on line 1. Over the past approximately 7

years the company has observed the available number of hours per week for the two lines, and the observations

are provided in the attached le LineTimes.csv. A total of 56 hours per week, for the two lines combined, can

be bought from a service provider at a cost of \$1200/h. Idle hours on line 1 must be used to produce raw

material. At the end of the week, a maximum of 50 units can be stored and each unit is valued at \$350.

Answer the following questions.

a) If the company wants to maximise weekly prot, formulate the decision problem as a stochastic program.

b) Solve the expected value model.

c) If it is given that you have to adhere to the available line times 95% of the time, nd the best product mix.

d) The plant can run at most 10 hours of overtime per line at a cost of \$900/h. Any raw material units in

excess of the capacity must be destroyed at a cost of \$85/unit. Find the best product mix.

e) Comment on the reliability of the models.

 line1 line2 1 123.7194 106.016 2 117.3595 107.0607 3 117.206 107.0036 4 126.6537 106.7803 5 127.1677 107.2586 6 108.2213 106.8765 7 141.3727 105.6488 8 140.9127 102.0759 9 112.6826 106.1999 10 118.6226 106.8649 11 122.5312 101.687 12 147.6067 104.5211 13 141.1965 110.4175 14 124.2985 107.4781 15 118.1845 108.9517 16 120.1861 108.6206 17 128.5674 107.6168 18 119.5912 106.8713 19 108.9195 110.902 20 113.76 110.3663 21 113.8151 112.8255 22 108.432 110.5945 23 113.1373 108.6487 24 118.5483 109.4957 25 112.8883 108.9186 26 106.8483 108.7358 27 115.0206 108.2302 28 108.906 106.3062 29 118.9149 108.9653 30 145.3249 107.684 31 102.9496 110.4406 32 123.2944 106.4192 33 118.3686 106.6721 34 132.9443 108.2661 35 146.1309 105.2575 36 113.7964 111.969 37 111.7626 106.6632 38 155.1842 104.5727 39 122.1077 114.2804 40 130.3702 104.8103 41 141.5985 104.4644 42 116.7861 106.7674 43 117.436 111.0593 44 120.1757 108.1997 45 125.1092 105.761 46 105.3622 110.6857 47 109.6553 103.8312 48 117.9505 108.0172 49 123.2171 108.1026 50 117.1657 112.157 51 143.8485 106.4216 52 149.636 111.1028 53 137.8911 109.9562 54 111.1402 104.5839 55 120.066 97.41807 56 143.9843 108.9387 57 121.4864 110.3017 58 123.7571 109.0176 59 107.5119 111.1394 60 108.5155 110.8205 61 100.3736 108.2684 62 118.8496 114.6236 63 129.3622 108.7911 64 130.6518 109.7858 65 130.7776 106.6153 66 127.1083 101.7676 67 154.0357 106.8637 68 129.162 107.2969 69 136.3561 110.936 70 142.3734 108.6427 71 130.1561 109.4654 72 106.6527 111.052 73 113.2807 103.2451 74 108.6965 102.04 75 152.5143 107.787 76 135.0795 110.4766 77 131.7102 110.3692 78 135.143 107.2122 79 119.4103 112.3601 80 126.6822 113.2096 81 151.5627 111.3766 82 117.6153 110.6037 83 109.904 110.247 84 121.9741 105.5584 85 107.6241 108.572 86 151.9012 111.6874 87 147.4743 109.035 88 135.9943 108.6702 89 120.43 113.8156 90 112.6237 107.3972 91 135.1927 111.2005 92 130.6343 106.927 93 117.709 98.64739 94 129.5451 106.2211 95 147.0611 114.4001 96 132.2998 111.5197 97 106.7732 111.9756 98 123.9423 106.2101 99 145.9043 109.2959 100 114.3695 108.523 101 150.9142 109.9183 102 113.0484 107.3009 103 137.3287 103.4561 104 118.7472 113.016 105 136.4962 110.107 106 122.0747 107.2185 107 118.3318 108.518 108 153.2655 110.9501 109 112.9004 106.1281 110 110.1912 105.8302 111 135.004 105.6479 112 117.9055 104.6723 113 113.1098 108.0931 114 127.3675 110.0309 115 118.6465 109.0723 116 120.6639 117.0075 117 112.608 107.2612 118 131.796 107.6872 119 136.1729 108.476 120 109.1827 111.3582 121 117.274 112.092 122 117.3989 106.5937 123 135.3774 111.0998 124 110.6241 106.269 125 118.8344 105.5086 126 129.9966 107.7149 127 106.7522 105.9588 128 97.98051 107.4044 129 139.1154 110.7679 130 126.8116 103.3127 131 110.0134 106.1353 132 135.1617 105.798 133 118.404 110.9059 134 144.6813 105.7239 135 139.9603 109.8971 136 104.022 109.8045 137 111.1768 100.3105 138 121.8455 110.0066 139 124.6052 102.4602 140 128.1123 106.6434 141 134.6186 101.1604 142 101.0249 111.743 143 126.8839 104.5711 144 132.1719 108.3161 145 129.3179 106.3951 146 102.7578 107.2649 147 141.2667 110.5617 148 125.7551 102.5195 149 100.2079 106.1502 150 108.9905 105.4859 151 104.8892 110.4011 152 116.4509 105.4286 153 116.9453 109.1921 154 130.8368 107.5716 155 139.6929 106.9321 156 113.669 105.0308 157 115.709 104.4699 158 112.7647 108.2518 159 136.2435 108.394 160 111.7798 107.685 161 125.1035 108.6813 162 107.032 107.5194 163 109.494 107.4713 164 128.2317 107.5643 165 113.7407 105.6968 166 131.5188 106.4754 167 125.3523 108.5463 168 121.0521 109.3238 169 118.9632 106.8935 170 119.9488 103.785 171 114.1417 106.8845 172 122.7955 108.1491 173 117.5067 112.2333 174 131.9754 109.846 175 114.7129 109.8354 176 110.5316 103.548 177 137.7302 108.5257 178 126.7493 105.458 179 142.3054 111.3693 180 133.3496 108.6949 181 148.9848 105.9005 182 149.0221 109.798 183 99.43433 114.1101 184 124.8203 108.4912 185 133.7033 104.4219 186 106.1981 100.2323 187 135.958 102.1554 188 148.6663 111.4081 189 108.8523 107.0523 190 134.9205 103.5163 191 138.453 107.3219 192 104.7262 110.4895 193 99.98908 103.8641 194 120.1989 114.7006 195 116.2007 108.9416 196 129.1934 102.6906 197 102.4423 107.4312 198 101.8545 105.0886 199 137.0068 107.6299 200 127.2799 108.8257 201 122.3079 109.6004 202 151.636 107.5318 203 134.3511 108.1712 204 130.368 116.0853 205 142.6315 107.0548 206 121.9085 103.3567 207 119.3323 101.5437 208 123.2148 105.8041 209 146.3416 100.7847 210 98.32865 104.1872 211 149.6443 110.4484 212 129.838 101.3789 213 120.9936 100.891 214 143.158 111.1563 215 117.7748 106.2273 216 115.2436 107.1226 217 127.9779 109.6497 218 113.6136 114.6441 219 113.8631 110.297 220 134.4797 103.0756 221 118.2722 106.1311 222 102.2335 109.6041 223 113.2959 112.1714 224 121.9082 104.9504 225 143.1142 108.9678 226 136.8585 105.8056 227 117.6956 107.2994 228 116.7278 106.5266 229 104.5992 106.6818 230 105.5803 108.2207 231 124.5136 110.7189 232 132.4642 108.4622 233 97.92918 107.1014 234 122.3738 107.7227 235 135.7589 110.0184 236 106.7861 110.2414 237 150.7215 106.8125 238 118.3906 109.1849 239 140.8336 109.5716 240 124.4483 109.4436 241 112.0195 109.6124 242 118.9617 110.4385 243 111.1105 100.7233 244 129.4419 102.4872 245 135.2798 105.0163 246 148.2855 109.5771 247 129.3579 108.6096 248 113.3744 103.2471 249 122.7334 108.3104 250 117.938 111.6019 251 148.1977 106.265 252 125.9089 109.3908 253 120.2952 112.5251 254 124.5914 109.9248 255 120.5195 105.005 256 114.7883 112.4402 257 131.1999 105.6394 258 157.9168 110.0817 259 147.8474 106.6815 260 132.7334 113.7339 261 113.4506 103.3865 262 141.1303 108.0212 263 123.3333 108.5055 264 138.172 107.2505 265 120.5264 107.7176 266 113.2519 107.8881 267 103.3399 113.2303 268 120.2441 109.2978 269 113.2651 107.1134 270 159.2402 109.0954 271 114.6304 101.6504 272 135.5953 110.4714 273 145.732 106.8406 274 141.9865 110.6212 275 153.181 111.658 276 100.7492 110.0625 277 154.7532 108.7032 278 111.2475 108.1659 279 108.2962 109.3359 280 107.7961 108.5765 281 159.1554 112.4021 282 104.1591 110.6547 283 115.2436 105.3268 284 115.8448 107.5106 285 120.1204 105.8491 286 141.1414 109.7015 287 128.9964 107.0237 288 132.5965 114.9669 289 114.1913 106.2807 290 110.2304 107.9192 291 126.0201 105.6793 292 129.8751 110.5542 293 125.6607 108.6704 294 139.3905 102.6171 295 124.7485 104.4055 296 138.4633 107.6978 297 126.5653 103.8898 298 112.9485 104.8846 299 141.7069 104.4054 300 148.0592 107.9928 301 124.8302 108.3212 302 125.9052 108.028 303 114.8848 108.5327 304 123.7867 105.2096 305 130.5349 107.8001 306 128.8041 106.0872 307 101.7364 104.2591 308 130.2397 109.776 309 135.7723 105.8084 310 105.3935 105.6829 311 113.9679 103.2266 312 117.3234 107.885 313 118.0139 105.7584 314 113.2044 106.1432 315 113.3881 106.8899 316 145.8231 107.8448 317 156.4658 106.9909 318 136.6749 109.232 319 144.5577 111.7906 320 122.832 109.7595 321 129.2767 108.8408 322 116.4054 109.3247 323 146.948 104.32 324 138.1987 108.6868 325 106.5052 111.9166 326 102.8354 108.883 327 126.6054 111.3332 328 118.5751 108.8962 329 119.0175 110.1977 330 126.6357 105.7716 331 138.814 109.9424 332 108.107 102.0895 333 113.333 109.1683 334 108.6639 105.1311 335 121.0321 104.9769 336 130.8679 111.8125 337 134.5171 104.0384 338 113.5162 108.9591 339 102.72 106.5287 340 127.7254 104.9707 341 129.2911 110.1595 342 111.4415 105.1417 343 136.489 105.6943 344 133.1458 106.3663 345 159.0287 108.5854 346 127.7691 98.4113 347 105.0539 107.5563 348 133.3591 106.8073 349 116.6054 104.8982 350 119.4875 105.7503 351 101.8014 104.1209 352 134.8621 109.0642 353 111.7118 103.1745 354 137.2647 107.6311 355 123.4962 109.7395 356 130.5782 110.3801 357 106.4009 101.6831 358 144.4666 107.8094 359 114.2166 107.7226 360 107.3446 108.9517 361 133.5548 104.6741 362 129.0472 111.7283 363 116.0153 107.4756 364 110.762 109.4401
8d3YA9FFPYknzq
line1 line2
1 123.7194 106.016
2 117.3595 107.0607
3 117.206 107.0036
4 126.6537 106.7803
5 127.1677 107.2586
6 108.2213 106.8765
7 141.3727 105.6488
8 140.9127 102.0759
9 112.6826 106.1999
10 118.6226 106.8649
11 122.5312 101.687
12 147.6067 104.5211
13 141.1965 110.4175
14 124.2985 107.4781
15 118.1845 108.9517
16 120.1861 108.6206
17 128.5674 107.6168
18 119.5912 106.8713
19 108.9195 110.902
20 113.76 110.3663
21 113.8151 112.8255
22 108.432 110.5945
23 113.1373 108.6487
24 118.5483 109.4957
25 112.8883 108.9186
26 106.8483 108.7358
27 115.0206 108.2302
28 108.906 106.3062
29 118.9149 108.9653
30 145.3249 107.684
31 102.9496 110.4406
32 123.2944 106.4192
33 118.3686 106.6721
34 132.9443 108.2661
35 146.1309 105.2575
36 113.7964 111.969
37 111.7626 106.6632
38 155.1842 104.5727
39 122.1077 114.2804
40 130.3702 104.8103
41 141.5985 104.4644
42 116.7861 106.7674
43 117.436 111.0593
44 120.1757 108.1997
45 125.1092 105.761
46 105.3622 110.6857
47 109.6553 103.8312
48 117.9505 108.0172
49 123.2171 108.1026
50 117.1657 112.157
51 143.8485 106.4216
52 149.636 111.1028
53 137.8911 109.9562
54 111.1402 104.5839
55 120.066 97.41807
56 143.9843 108.9387
57 121.4864 110.3017
58 123.7571 109.0176
59 107.5119 111.1394
60 108.5155 110.8205
61 100.3736 108.2684
62 118.8496 114.6236
63 129.3622 108.7911
64 130.6518 109.7858
65 130.7776 106.6153
66 127.1083 101.7676
67 154.0357 106.8637
68 129.162 107.2969
69 136.3561 110.936
70 142.3734 108.6427
71 130.1561 109.4654
72 106.6527 111.052
73 113.2807 103.2451
74 108.6965 102.04
75 152.5143 107.787
76 135.0795 110.4766
77 131.7102 110.3692
78 135.143 107.2122
79 119.4103 112.3601
80 126.6822 113.2096
81 151.5627 111.3766
82 117.6153 110.6037
83 109.904 110.247
84 121.9741 105.5584
85 107.6241 108.572
86 151.9012 111.6874
87 147.4743 109.035
88 135.9943 108.6702
89 120.43 113.8156
90 112.6237 107.3972
91 135.1927 111.2005
92 130.6343 106.927
93 117.709 98.64739
94 129.5451 106.2211
95 147.0611 114.4001
96 132.2998 111.5197
97 106.7732 111.9756
98 123.9423 106.2101
99 145.9043 109.2959
100 114.3695 108.523
101 150.9142 109.9183
102 113.0484 107.3009
103 137.3287 103.4561
104 118.7472 113.016
105 136.4962 110.107
106 122.0747 107.2185
107 118.3318 108.518
108 153.2655 110.9501
109 112.9004 106.1281
110 110.1912 105.8302
111 135.004 105.6479
112 117.9055 104.6723
113 113.1098 108.0931
114 127.3675 110.0309
115 118.6465 109.0723
116 120.6639 117.0075
117 112.608 107.2612
118 131.796 107.6872
119 136.1729 108.476
120 109.1827 111.3582
121 117.274 112.092
122 117.3989 106.5937
123 135.3774 111.0998
124 110.6241 106.269
125 118.8344 105.5086
126 129.9966 107.7149
127 106.7522 105.9588
128 97.98051 107.4044
129 139.1154 110.7679
130 126.8116 103.3127
131 110.0134 106.1353
132 135.1617 105.798
133 118.404 110.9059
134 144.6813 105.7239
135 139.9603 109.8971
136 104.022 109.8045
137 111.1768 100.3105
138 121.8455 110.0066
139 124.6052 102.4602
140 128.1123 106.6434
141 134.6186 101.1604
142 101.0249 111.743
143 126.8839 104.5711
144 132.1719 108.3161
145 129.3179 106.3951
146 102.7578 107.2649
147 141.2667 110.5617
148 125.7551 102.5195
149 100.2079 106.1502
150 108.9905 105.4859
151 104.8892 110.4011
152 116.4509 105.4286
153 116.9453 109.1921
154 130.8368 107.5716
155 139.6929 106.9321
156 113.669 105.0308
157 115.709 104.4699
158 112.7647 108.2518
159 136.2435 108.394
160 111.7798 107.685
161 125.1035 108.6813
162 107.032 107.5194
163 109.494 107.4713
164 128.2317 107.5643
165 113.7407 105.6968
166 131.5188 106.4754
167 125.3523 108.5463
168 121.0521 109.3238
169 118.9632 106.8935
170 119.9488 103.785
171 114.1417 106.8845
172 122.7955 108.1491
173 117.5067 112.2333
174 131.9754 109.846
175 114.7129 109.8354
176 110.5316 103.548
177 137.7302 108.5257
178 126.7493 105.458
179 142.3054 111.3

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