A clothing manufacturer makes coats, shirts, and slacks. The time required for cutting, sewing, and packaging each item is shown in the table. How many of each should be made to use all available labor hours? Coats Shirts Slacks Time available Cutting 20 min 15 min 10 min 120 hr Sewing 60 min 30 min 24 min 310 hr Packaging 5 min 12 min 6 min 58 hr

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The total time available for cutting is 120 hours. The time required for cutting 1 coat is 20 minutes, or 1/3 hour. So, the number of coats that can be cut in 120 hours is 120 / (1/3) = 360 coats.The total time available for sewing is 310 hours. The time required for sewing 1 shirt is 30 minutes, or 1/2 hour. So, the number of shirts that can be sewn in 310 hours is 310 / (1/2) = 620 shirts.The total time available for packaging is 58 hours. The time required for packaging 1 pair of slacks is 6 minutes, or 1/10 hour. So, the number of pairs of slacks that can be packaged in 58 hours is 58 / (1/10) = 580 pairs of slacks.The smallest number of items that can be made is 180 coats, 140 shirts, and 150 slacks.

A Clothing Manufacturer Makes Coats, Shirts, and Slacks