Each week at a furniture factory, 2000 work hours are available in the construct

Question

Each week at a furniture factory, 2000 work hours are available in the construction department, 1400 work hours in the painting department, and 1300 work hours in the packing department. Producing a chair requires 2 hours of construction, 1 hour of painting, and 2 hours for packing. Producing a table requires 4 hours of construction, 3 hours of painting, and 3 hours for packing. Producing a chest requires 8 hours of construction, 6 hours of painting, and 4 hours for packing. If all available time is used in every department, how many of each item are produced each week?

Show your reasoning.

Explanation / Answer

this isn't probability? (unless I'm missing something) so we get 2000c, 1400p, 1300P. Let's use 2000x, 1400y, 1300z for the rest of this. a=2x+1y+2z b=4x+3y+3z c=8x+6y+4z 2000=2a+4b+8c (rewrite the columns going down as = to it) 1400=1a+3b+6c 1300=2a+3b+4c then we can just use a calculator or manipulate the rows. I get: a = 200, b = 100, c = 150

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