Question

The distances (in miles) between UW Campuses of Platteville, Whitewater, Stout, Milwaukee, and Baraboo are shown in the table below (not all are accurate and reflective of actual distances). We want to connect these campuses with fiber optic cable. Direct connections between Platteville and Whitewater, and Baraboo and Stout are not possible. What is the minimum length of cable required? 12 79 Platteville Whitewater Stout Milwaukee Baraboo Platteville 217 164 58 Whitewater 132 290 201 Stout 290 113 303 Milwaukee 113 196 Baraboo 58 79 303 196 Total length of wire required: [length] miles Just enter the number. Do not enter comma separators or decimals.

Answer 1

-clearly problem is one of assignment (which is a special case of LP) sure that restricted I restricted To make scenario scenario do not show up in do not final optimal solution, we have to penalize them by assigning large values (since we will be minimizing so they will never show up in optimal solution) Also boxes with dashed lines are penalized by large numbers, o Let us assume this number be 500 (since all other numbers are lower than this one) 500 500 217 164 58) 500 500 290 201 79 stept select minimum of each column and substract it from corresponding column elements 217 290 500 113 500 164 201 113 500 196 Step 2 then select minimum of each you and substract it from corresponding row elements. 58 79 196 5vo min of each column mindre 412 421 104-1 YOO 442 421 104 51 442 421 177 68 1421 4w0 156 67 0 159 211 387 0 442 159-211- 3870 - 442 106 122 0 337 138 -106-122.0 +387 138 0 387 33 442 107073815 33 1442 Stop3 draw minimum number of lines Ceither vertical or horizontal) to cover all zeros. In number of lines are less than no. of columns or rous then solution re not optimal and if no of lines equals no. of colums/rows then solution is optimal and assignment com be done. since number of lines is 4 and column/row are 5 so not optional. stop 4 - Select minimum entry from rest elements and subtract it from remaining and add it to elements at intersection of lines and repeat from step 1.

338 317 TO 338/317 / 106 106 fo6 340 349 105 16, 317296 521 160 2012 140 52 16 0 159 211 387 0 4931 106) 153 334 0 493 152 334 min. O 493) 1106 122 o 382 1981) 1106 122 of 440 292 16 440 242 931 63 493 337 136/546 493 242 652 for this matrix trimam Namber of mosquired 5 = o. of row/alumn. But since no feasible assignment is possible so repeat step & again. 232 231 0 211 190 52 16 52 334 403 These are final assignments and hence minimum optimal distance 162+ 79+217 +13+79 (from original matrix corresponding to assigned cells) 552 © 1932426