XLB Sports has 30 franchises (teams).Although most of the teams make an annual profit, some teams report losses.An owner of a team that loses money can still make a profit when he sells the franchise since equity increases have been greater than reported losses.XLB has requested a model to determine which, if any, franchises should be eliminated.The costs associated with team elimination include the buyout of the owner, paying off existing contracts such as ballpark leases, and anticipated legal costs.The objective function is the overall profit of XLB.Because all teams must play on the same day, the number of teams must be an even number.Some teams may lose money at home but help other teams by drawing well in road games. Which of the following is true?
A)Teams reporting a loss should be eliminated.
B)You should use binary variables in a mixed integer model.
C)The problem can be solved by solving 30 team integer linear programming models.
D)The problem cannot be modeled.

Question

Quizplus · Accepted Answer

Since the number of teams must be an even number, binary variables can be used to model whether a team is present or eliminated. This problem can be formulated as a mixed integer linear programming model with binary variables for team elimination and continuous variables for profit and costs. By minimizing the costs associated with elimination while maximizing the overall profit of XLB, the model can determine which franchises should be eliminated to maximize overall profitability.

XLB Sports Has 30 Franchises (Teams)