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December 13th, 2016, 08:09 PM   #1
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System of Equations

A company has 4 factories that each produce knee, hip, shoulder, and spinal implants made of titanium. The daily production of each factory for every 10 kg of titanium is: (Factory A; 7 knee, 5 hip, 3 shoulder, 4 spinal), (Factory B; 1 knee, 5 hip, 22 shoulder, 4 spinal), (Factory C; 8 knee, 1 hip, 9 shoulder, 1 spinal), (Factory D; 7 knee, 2 hip, 8 shoulder, 2 spinal).

Suppose the company can only purchase titanium in 10 kg units. What is the system of equations that describes the daily production of each factory?

I initially came up with the system of equations as:
7k+5h+3sh+4s=10;
1k+5h+22sh+4s=10;
8k+1h+9sh+1s=10;
7k+2h+8sh+2s=10;

I was told this is not the correct system of equations, and that I should think in terms of input/output. Maybe they should be equated to separate variables instead of using 10? Im kind of stuck here. Thanks in advance.
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December 14th, 2016, 05:04 AM   #2
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I can see no reason why those should be equal to 10. You are told those are the number of implants each factory can make per 10 kg of titanium, not that they added to 10 kg. Also the problem said the company can only purchase titanium in 10kg units, not that it can only purchase 10 kg and not 10kg for each factory.
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