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**Linear Programming - Cabinets**

By Stephanie Scott

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Problem Your company produces cabinets using two different processes. The number of assembly hours required for each process is listed in the table below. You can use up to 3000 hours of machine time, up to 3600 hours of skilled labor, and up to 3600 hours of unskilled labor. The profit from Process A is $50 per cabinet and the profit from Process B is $70 per cabinet. How many cabinets should you make with each process to obtain a maximum profit? Process A Process B Machine Time Skilled Labor Unskilled Labor

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Variables Process A = X Process B= Y

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**Constraints x+2y < 3000 3x+y < 3600 2x+2y < 3600 X > 0**

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**Objective Function In Process A we make $50 In Process B we make $70**

So the objective function is P=X50+Y70

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Graph On paper

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**Max & Min Points (0, 1500), (600, 1200), (900, 900), and (1200,0)**

Plug the points into the objective function P=X50+Y70 P=(o)50+(1500)70, =105000 P=(600)50+(1200)70, =114000, Max P=(900)50+(900)70, = P=(1200)50+(0)70, = 60000, Min

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Conclusion I learned that in reality that you can use linear programming to answer questions in real life situations such as finding the min or the max on a profit. 600 cabinets in Process A and 1200 cabinets in Process B will make the most money.

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