An aluminum plant turns out two types of aluminum x1 and x2. Type 1 takes 6 hours for melting, 3 hours for rolling, and 1 hour for cutting. Type 2 takes 2 hours for melting, 5 hours for rolling, and 4 hours for cutting. The plant has 36 hours of melting time available, 30 hours of rolling time, and 20 hours of cutting time. The profit margin is $10 for x1 and $8 for x2. Reduce the data to equations and inequalities suitable for finding the profit-maximizing output mix.

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Maximize 10x18x2 subject to 6x1 + 2x2 36 (melting constraint) 3x1+5x230 (rolling constraint) x1+4x2 20 (cutting constraint). For a graphic solution, see Problem 7.10. X1, X20