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HW 7 Solutions

# HW 7 Solutions - Integer Programming Homework Solutions...

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STOR 112 1. (15 points) SuperDog is investigating 5 possible sites for its carts in the very competitive hot dog cart business in the financial district of Manhattan. It has so confident in the deliciousness of its hot dogs that it has decided that in order run its rival, WienerMax, out of its territory, it must place at least one hot dog cart within 3 blocks of each of the 4 outlets run by WienerMax. The table below gives the distance between the 5 sites and each of the existing WienerMax outlets, as well as the estimated cost of opening a SuperDog cart at the 5 sites. Distance to WienerMax cart (blocks) Estimated cost Possible location: A B C D Nassau St. (N) 3.5 6.0 2.5 6.5 \$1500 Broadway (BW) 1.5 2.5 5.0 6.0 \$2200 Wall St. (W) 2.0 8.0 3.5 1.0 \$2900 Broad St. (BS) 4.5 2.5 3.5 2.5 \$1600 South St. (S) 5.0 6.0 1.5 4.5 \$1200 a) Formulate an integer program to help SuperDog determine where to establish its new carts, at minimum estimated cost, if it is to be an effective competitor to WienerMax. The variables are all binary: N is 1, if we open a stand at Nassau street, 0 if not. The other variables are defined similarly. min 15N + 22BW + 29W + 16BS + 12S st BW + W 1 WienerMax outlet A BW + BS 1 WienerMax outlet B N + S 1 WienerMax outlet C W + BS 1 WienerMax outlet D N, BW, W, BS, S all binary b) Interpret your solution. Superdog should open locations at Broadway, Broad St., and South St.

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HW 7 Solutions - Integer Programming Homework Solutions...

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