A company makes industrial control units. They have a new line of products. Making each "Argon I" unit needs 6M and 3N. Each "Argon II" unit needs 10M and 8N. The company obtains 760M and 500N each day. How many units of each model can the company make daily? All parts are used.

Question

asnaseer · Answer

lets call Argon I unit $a_1$ and Argon II unit $a_2$. we can then write:$$a_1=6M+3N$$$$a_2=10M+8N$$so if we make 'p' Argon I units and 'q' Argon II units, we can write:$$pa_1+qa_2=760M+500N$$$$p(6M+3N)+q(10M+8N)=760M+500N$$
can you solve from here on?

anonymous · Answer

I'm not really sure if I can, and since we're in Matrices and Linear Equation Systems I think this was supposed to be done that way.

asnaseer · Answer

yes - it CAN be done exactly that way if you follow through from where I left off.

anonymous · Answer

Sorry, but I'm really lost and can't quite seem to understand how to arrange these numbers..

asnaseer · Answer

Let me show you the next few steps:$$6pM+3pN+10qM+8qN=760M+500N$$$$(6p+10q)M+(3p+8q)N=760M+500N$$so:$$6p+10q=760$$$$3p+8q=500$$

asnaseer · Answer

now just solve to find p and q

anonymous · Answer

Thank you very much, I have a similar one, hope I don't need to ask again to get it solved.

asnaseer · Answer

I'm glad you got there in end - well done!