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# Mathematics - Linear Operators

Expedition Outfitters manufactures a variety of specialty clothing for hiking, skiing, and mountain climbing. They decided to begin production on two new parkas designed for use in extremely cold weather. The names selected for the two models are the Mount Everest Parka and the Rocky Mountain Parka. Their manufacturing plant has 120 hours of cutting
time and 120 hours of sewing time available for producing these two parkas. Each Mount Everest Parka requires 30 minutes of cutting time and 45 minutes of sewing time, and each Rocky Mountain Parka requires 20 minutes of cutting time and 15 minutes of sewing time. The labor and material cost is \$150 for each Mount Everest Parka and \$50 for each Rocky
Mountain Parka, and the retail prices through the firm's mail order catalog are \$250 for the Mount Everest Parka and \$200 for the Rocky Mountain Parka. Because management believes that the Mount Everest Parka is a unique coat that will enhance the image of the firm, they have specified that at least 20% of the total production must consist of this
model. Assuming that Expedition Outfitters can sell as many coats of each type as they can produce, how many units of each model should they manufacture to maximize the total profit contribution?

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