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Shirtstop makes T-shirts with logos and sells them in its chain of retail stores. It contracts with 2 different plants - one in Puerto Rico and one in the Bahamas. The shirts from the plant in Puerto Rico cost $0.46 apiece, and 9% of them are defective and can't be sold. The shirts from the plant in the Bahamas cost only $0.35 each, but they have an 18% defective rate. Shirtstop needs 3,500 shirts. To retain its relationship with the two plants, it wants to order at least 1,000 shirts from each plant. It would also like at least 88% of the shirts it receives to be salable.
a) Formulate the linear programming (LP) model for this problem by stating the decision variables, writing the objective function, and all the relevant constraints.
Decision VariablesLet X1 represent the number of shirts purchased from Puerto RicoLet X2 represent the number of shirts purchased from the BahamasObjective FunctionMinimize Z = .46X1 + .35X2ConstraintsX1 + X2 ? 3500 Desired shirts constraintX1 ? 1000 Minimum from PR constraintX2 ?1000 Minimum from the Bahamas constraint
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