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A furniture factory has 2230 machine hours available each week in the cutting​ department, 1470 hours...

A furniture factory has 2230 machine hours available each week in the cutting​ department, 1470 hours in the assembly​ department, and 2960 in the finishing department. Manufacturing a chair requires 0.3 hours of​ cutting, 0.5 hours of​ assembly, and 0.6 hours of finishing. A cabinet requires 0.8 hours of​ cutting, 0.3 hours of​ assembly, and 0.1 hours of finishing. A buffet requires 0.2 hours of​ cutting, 0.1 hours of​ assembly, and 0.9 hours of finishing. How many​ chairs, cabinets, and buffets should be produced in order to use all the available production​ capacity?

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