Gales Products manufactures ribbon for thermal transfer printing, which transfers ink from a ribbon onto paper through a combination of heat and pressure. Different types of printers use different sizes of ribbons. The company has forecasted demands for seven different ribbon sizes as shown in the table to the right. The rolls from which ribbons are cut are 900 mm in length. Scrap is valued at $ 0.07 per millimeter. Generate 10 different cutting patterns so that each

size can be cut from at least one pattern. Use your data to construct and solve an optimization model for finding the number of patterns to cut to meet demand and minimize trim loss.

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Forecast (Rolls) Size 60 mm 83 mm 102 mm 110 mm 120 mm 130 mm 165 mm 1,620 520 840 2,640 500 740 680