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Optimal Solution for Clothing Retailer

A company makes three types of shirts: Athletic, Varsity, and Surfer. The shirts are made from different combinations of cotton and rayon. The cost per yard of cotton is $5 and of rayon is $7. The company can receive up to 4000 yards of cotton and 3000 yards of rayon per week. The table below shows relevant manufacturing information:

Shirt Fabric Requirement/Minimum Weekly Contracts Maximum Weekly Demand Selling Price
Athletic 1.00/At least 60% cotton 500 600 $30
Varsity 1.20/No more than 30% rayon 650 850 $40
Surfer 0.90 Up to 80% cotton 300 700 $36

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Solution Preview

Please refer attached file for complete solution.

the total number of Athletic shirts produced be A
the total number of Varsity shirts produced be V
the total number of Surfer shirts produced be S

Cotton cloth used in Athletic shirts be Xca
Cotton cloth used in Varsity shirts be Xcv
Cotton cloth used in Surfer shirts be Xcs

Rayon cloth used in Athletic shirts be Xra
Rayon cloth used ...

Solution Summary

Solution builds a linear programming model in the given case and determines the optimal output level of Athletic, Varsity and Surfer shirts. Solution is determined with the help of "Solver" in MS Excel.