Target Shirt Company makes three varieties of shirts: Collegiate, Traditional, and European. These shirts are made from different combinations of cotton and polyester. The cost per yard of unblended cotton is $4 and for unblended polyester is $3. Target can receive up to 4,100 yards of raw cotton and 3,100 yards of raw polyester fabric weekly. The table below gives pertinent data concerning the manufacture of the shirts. Shirt Total Yards Fabric Requirement Weekly Contracts Weekly Demand Selling Price Collegiate 1 At least 50% cotton 500 600 $13 Traditional 1.2 European 0.95 No more than 20% polyester As much as 80% polyester 650 850 $14 280 675 $17 Formulate this blending problem as a linear program. (Let S, = the total number of shirt style j produced, F; = the number of yards of fabric type i produced, X;; = the number of yards of fabric type i blended into shirt style j produced where i = 1 (cotton), 2(polyester) and j = 1 (collegiate), 2(traditional), or 3(European). Max collegiate shirts made compared to fabric purchased traditional shirts made compared to fabric purchased European shirts made compared to fabric purchaced total yardage of materials cotton total yardage of materials polyester