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# Formulating an Integer Linear Program

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M. Quinn is preparing for a 12 day dog sled race. He owns eight dogs, but the race will allow only five dogs - the four pack dogs and the lead dog. M. Quinn has developed a test to measure the endurance of each dog. The endurance score for each dog and the amount of ALPO each dog requires per day is listed in the table below. M. Quinn wants to select the five dogs that will give the team the maximum endurance score subject to the following constraints.

1 Only 62 ounces of ALPO will be available each day.
2 At least two of the five dogs selected must have lead dog ability
3 Ren and Snippy are very close. Thus if Ren is selected for the team, Snippy must also be selected for the team and vice versa.
4 Snoopy and Snert hate each other's guts. Therefore, either Snoopy can be on the team, Snert can be on the team, or neither of them can be on the team. However, both of them cannot be on the team.

Formulate the integer LP problem to determine which dogs should be selected in order to maximize endurance rating.

Dog Endurance rating Ounces of Alpo/day Lead dog ability
Bolivar 50 12 Yes
Pluto 90 11 No
Ren 65 10 No
Lassie 95 15 Yes
Odie 60 8 No
Snippy 65 11 No
Snoopy 90 15 Yes
Snert 80 18 No

Which dogs should not be included on the team? __________

What is the total maximum endurance for the team? ________

How many ounces of ALPO will actually be needed each day? _________