Formulating and solve a problem as an integer programming problem to determine the number of DCs required to meet CSL = 90% - open to bidding

I want this to be solved like in 2 hours: Al-Souks is a mail-order DVD-rental company. You choose which DVDs to rent on Al-Souks’ web site, and the company mails the DVDs to you. When you've finished watching the movies, you mail them back to Al-Souks. Al-souks’ business plan depends on fast shipping times (otherwise customers will get impatient). But overnight delivery services like FedEx are prohibitively expensive. Instead, Al-Souks has decided to open enough DCs to so that roughly 90% of their customers enjoy 1-day delivery times. In this problem, you will formulate and solve a model to determine where Al-Souks should locate DCs to ensure that a desired percentage of the population is within a 1-day mailing range while minimizing the fixed cost to open the DCs. (You may assume that the per-unit cost of processing and shipping DVDs is the same at every DC.) a. Formulate the following problem as an integer programing problem: we are given a set of cities, as well as the population of each city and the fixed cost to open a DC in that city. The objective is to decide in which cities to locate DCs in order to minimize the total fixed cost while also ensuring that at least a fraction of the population is within a 1-day mailing range. Define your notation clearly, and indicate which items are parameters (inputs) and which are decision variables. Explain each of your constraints in words. b. Implement your model using Lingo. Solve the problem using the following data set which gives the locations and populations of the 14 cities as well as the average annual fixed cost to open a DC in the city. The distance between each pair of cities is given. Assume that two cities are within 1-day mailing radius if they are no more than 500 KM apart. c. Using the data and a coverage percentage of α=0.9, find the optimal solution to the DC location problem. Include a printout of your model in your solution. Report the total cost of your solution and the total number of DCs. City Population Fixed Cost 1 81036 840000 2 38053 760000 3 29348 610000 4 20285 420000 5 15228 530000 6 13500 260000 7 12605 590000 8 23004 460000 9 11804 230000 10 96027 400000 11 92100 650000 12 80400 290000 13 19950 590000 14 76000 530000 1 2 3 4 5 6 7 8 9 10 11 12 13 14 1 0 2455 717 1419 77 2139 2426 1370 1582 488 2550 646 2570 835 2 2455 0 1745 1378 2395 366 116 1248 1209 1982 293 1812 339 2151 3 717 1745 0 938 666 1444 1723 799 1047 238 1833 163 1853 862 4 1419 1378 938 0 1343 1013 1298 224 188 1106 1603 866 1641 821 5 77 2395 666 1343 0 2076 2364 1298 1507 445 2497 584 2518 763 6 2139 366 1444 1013 2076 0 297 885 846 1681 608 1493 651 1789 7 2426 116 1723 1298 2364 297 0 1180 1123 1960 409 1781 455 2084 8 1370 1248 799 224 1298 885 1180 0 252 997 1447 762 1483 904 9 1582 1209 1047 188 1507 846 1123 252 0 1236 1446 999 1486 1009 10 488 1982 238 1106 445 1681 1960 997 1236 0 2066 240 2084 836 11 2550 293 1833 1603 2497 608 409 1447 1446 2066 0 1923 46 2337 12 646 1812 163 866 584 1493 1781 762 999 240 1923 0 1946 700 13 2570 339 1853 1641 2518 651 455 1483 1486 2084 46 1946 0 2370 14 835 2151 862 821 763 1789 2084 904 1009 836 2337 700 2370 0 Distances between cities