Just looking for help with the code based on the general LP. Thank you!
A manufacturing company makes a very popular line of 30 different widgets, whose demand is practically unrestricted. Their factory has 10 machines, labeled A through J and most machines can make most widgets (but not all). In the attached Excel file Case StudyOdata.xlsx, you will find two tabs. The tab labeled Cost has the cost per unit of making one widget in the corresponding machine. Note an X in the table means that that widget cannot be produced in that machine. This tab also has the revenue per unit of selling each widget. The tab labeled Time has the time per unit in seconds) that it takes to produce each unit of each widget in each machine. The company's factory works two 8-hour shifts per day, an average of 22 days per month. Each machine is available for that amount of time each month. Additionally, the company has estimated monthly operating costs for this factory are fixed at $ 1,000,000. This includes rent, overhead, salaries, etc. and only excludes the direct costs of producing the widgets. The company wants to produce the product mix that will maximize its profit, but also wants to satisfy the market's demand for variety, so they have decided to produce at least 2000 units of each widget every month. An additional complication is that each time that they want to make a widget in a machine they need to incur a setup. Setups do not cost any money, as they are performed by salaried employees and do not consume materials. However, they do take time. The company estimates that to setup a machine to make a widget takes about the time required to produce 100 units of that widget on that machine. This company has hired you as a consultant to help them plan their monthly production in order to maximize their profit. After some preliminary work, you have settled on four specific tasks that you are going to perform. Your job is to perform the four tasks and present a report with your findings. Tasks First, you will do a very rough estimation to account for setup times. You will ignore setup times completely, but try to make up for it by reducing the number of available working days from 22 to 20. You will also assume you can make fractions of widgets. 2. Code the LP you formulated above and solve it with the data provided. I recommend doing this in GUROBI with the Python API. Make sure your code is readable and thoroughly commented Summarize your results in the report, Maximize Z where Z= E(X(Xij)*Si for all j = {A,B,....J}) for all i ={1,2,... 30} - (Xij*Cij) for all i ={1,2,...30} - 1000000 Subject to E(Xij*Tij) for all i ={1,2,...30} = 2000 Xij >= 0 Cost Time F E 1.06 H 4.91 1.64 3.09 1.68 1.81 2.53 2.63 2.44 2.42 3.01 1.73 4.7 3.33 2.26 1.23 2.12 4.41 3.92 1.43 4.46 3.31 1.96 3.96 1.46 2.75 4.04 2.51 4.69 1.03 2.42 3.81 2.38 4.38 4.42 3.74 4.25 4.41 4.7 2.36 3.57 3.44 3.29 2.64 1.48 4,67 3.31 2.94 2.59 3.89 4.57 4.21 4.43 4.19 3.49 1.33 1.97 3.68 4.2 3.76 2.14 3.11 3.45 4.26 4.63 1.35 2.34 1.58 4.29 1.51 4.86 3.9 4.21 1.14 Sale Price 11.32 16.00 14.86 15.22 16.42 10.04 11.34 10.70 15.90 15.50 16.52 12.10 17.16 17.12 17.50 15.70 12.88 10.96 19.66 14.50 11.24 18.90 19.30 17.88 16.28 11.10 16,44 16,80 11.40 1.93 2.18 2.24 2.6 4.31 4.49 3.73 2.63 4.11 4.07 X 1.44 2.39 3.27 4.48 4.25 1.03 1.57 1.77 4.83 2.57 1.28 2.68 4,5 1.29 3.64 4.71 3.99 2.5 2.36 1.79 2.16 2.81 4.96 2.41 3.22 4.65 4.05 1.03 4.95 4.18 2.22 1.16 4,83 2.96 4.99 4.52 2.52 2.03 4.75 4.38 4.04 4.38 4.08 2.26 3.74 3.68 4.51 4.18 1.4 1.68 3.48 3.99 2.54 3.19 4.31 1.85 1.04 1.83 1.24 1.75 15.96 Cost Time D E F I B 499 303 341 240 410 202 391 362 408 354 540 216 597 C 287 99 533 152 474 590 169 176 320 415 379 422 303 124 174 506 581 311 X 75 273 517 570 303 147 196 260 427 555 460 386 407 234 366 358 340 204 390 281 130 582 506 524 566 80 597 356 160 471 438 104 263 251 518 155 268 325 260 193 477 353 486 311 145 584 416 460 344 59 279 245 173 232 441 477 462 444 201 465 237 342 315 270 130 553 340 342 216 444 262 597 X 321 316 228 325 293 194 490 384 517 510 488 111 156 548 174 X 427 339 242 231 157 112 122 566 44 100 305 232 293 237 144 39 53 486 81 589 561 246 189 402 206 243 583 105 193 452 X 388 492 220 275 132 244 270 248 496 583 392 229 A manufacturing company makes a very popular line of 30 different widgets, whose demand is practically unrestricted. Their factory has 10 machines, labeled A through J and most machines can make most widgets (but not all). In the attached Excel file Case StudyOdata.xlsx, you will find two tabs. The tab labeled Cost has the cost per unit of making one widget in the corresponding machine. Note an X in the table means that that widget cannot be produced in that machine. This tab also has the revenue per unit of selling each widget. The tab labeled Time has the time per unit in seconds) that it takes to produce each unit of each widget in each machine. The company's factory works two 8-hour shifts per day, an average of 22 days per month. Each machine is available for that amount of time each month. Additionally, the company has estimated monthly operating costs for this factory are fixed at $ 1,000,000. This includes rent, overhead, salaries, etc. and only excludes the direct costs of producing the widgets. The company wants to produce the product mix that will maximize its profit, but also wants to satisfy the market's demand for variety, so they have decided to produce at least 2000 units of each widget every month. An additional complication is that each time that they want to make a widget in a machine they need to incur a setup. Setups do not cost any money, as they are performed by salaried employees and do not consume materials. However, they do take time. The company estimates that to setup a machine to make a widget takes about the time required to produce 100 units of that widget on that machine. This company has hired you as a consultant to help them plan their monthly production in order to maximize their profit. After some preliminary work, you have settled on four specific tasks that you are going to perform. Your job is to perform the four tasks and present a report with your findings. Tasks First, you will do a very rough estimation to account for setup times. You will ignore setup times completely, but try to make up for it by reducing the number of available working days from 22 to 20. You will also assume you can make fractions of widgets. 2. Code the LP you formulated above and solve it with the data provided. I recommend doing this in GUROBI with the Python API. Make sure your code is readable and thoroughly commented Summarize your results in the report, Maximize Z where Z= E(X(Xij)*Si for all j = {A,B,....J}) for all i ={1,2,... 30} - (Xij*Cij) for all i ={1,2,...30} - 1000000 Subject to E(Xij*Tij) for all i ={1,2,...30} = 2000 Xij >= 0 Cost Time F E 1.06 H 4.91 1.64 3.09 1.68 1.81 2.53 2.63 2.44 2.42 3.01 1.73 4.7 3.33 2.26 1.23 2.12 4.41 3.92 1.43 4.46 3.31 1.96 3.96 1.46 2.75 4.04 2.51 4.69 1.03 2.42 3.81 2.38 4.38 4.42 3.74 4.25 4.41 4.7 2.36 3.57 3.44 3.29 2.64 1.48 4,67 3.31 2.94 2.59 3.89 4.57 4.21 4.43 4.19 3.49 1.33 1.97 3.68 4.2 3.76 2.14 3.11 3.45 4.26 4.63 1.35 2.34 1.58 4.29 1.51 4.86 3.9 4.21 1.14 Sale Price 11.32 16.00 14.86 15.22 16.42 10.04 11.34 10.70 15.90 15.50 16.52 12.10 17.16 17.12 17.50 15.70 12.88 10.96 19.66 14.50 11.24 18.90 19.30 17.88 16.28 11.10 16,44 16,80 11.40 1.93 2.18 2.24 2.6 4.31 4.49 3.73 2.63 4.11 4.07 X 1.44 2.39 3.27 4.48 4.25 1.03 1.57 1.77 4.83 2.57 1.28 2.68 4,5 1.29 3.64 4.71 3.99 2.5 2.36 1.79 2.16 2.81 4.96 2.41 3.22 4.65 4.05 1.03 4.95 4.18 2.22 1.16 4,83 2.96 4.99 4.52 2.52 2.03 4.75 4.38 4.04 4.38 4.08 2.26 3.74 3.68 4.51 4.18 1.4 1.68 3.48 3.99 2.54 3.19 4.31 1.85 1.04 1.83 1.24 1.75 15.96 Cost Time D E F I B 499 303 341 240 410 202 391 362 408 354 540 216 597 C 287 99 533 152 474 590 169 176 320 415 379 422 303 124 174 506 581 311 X 75 273 517 570 303 147 196 260 427 555 460 386 407 234 366 358 340 204 390 281 130 582 506 524 566 80 597 356 160 471 438 104 263 251 518 155 268 325 260 193 477 353 486 311 145 584 416 460 344 59 279 245 173 232 441 477 462 444 201 465 237 342 315 270 130 553 340 342 216 444 262 597 X 321 316 228 325 293 194 490 384 517 510 488 111 156 548 174 X 427 339 242 231 157 112 122 566 44 100 305 232 293 237 144 39 53 486 81 589 561 246 189 402 206 243 583 105 193 452 X 388 492 220 275 132 244 270 248 496 583 392 229
