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Rott Irony manufactures four types of light fixtures. A fancy lamp yields a profit of $100, takes 10 hours of labor and 2 hours of machine time, and requires 10 ft2 of sheet metal. An ornate lamp yields a profit of $150, takes 8 hours of labor and 3 hours of machine time and requires 20 ft2 of metal. The plain and rococo lamps each yield a $200 profit and involve 1 hour of machine time. However, the rococo lamp requires 20 hours of labor and 30 ft2 of metal, and plain lamp requires 10 hours of labor and 15 ft2 of metal. Rott must produce at least twice as many plain lamps as rococo ones. Only 1,000 hours of labor and 200 hours of machine time are available, and 5,000 ft2 of sheet metal are in inventory. Rott wishes to determine how many of each type of each lamp to make to maximize total profits. Formulate this problem as a linear program.
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