Machines in parallel

Oct 2010
58
3
Hey, I had this little optimization problem and I kinda feel like my solution was too simple - maybe someone here might want to check it out?

We have two machines, each capable of producing a product A. Machine 1 takes 14 minutes to finish, machine 2 takes 15 minutes. If the machines can work in parallel and independent of each other, how should we distribute the workload in order to minimize production time? We are to to produce 70 units in total.

So, what I did was just this:
It takes some total time T to finish all 70 units. During that time, machine 1 can complete T/14 units and machine 2 can complete T/15 units. We then know that

(T/14) + (T/15) = 70

Solve for T, and then divide that with 14 and 15 to find out how many should be produced in each machine, respectively. Of course, we have to round the results to the nearest reasonable integers.

I do get a fairly reasonable result and all, but I don't know... am I being too simplistic about this?
 
Feb 2014
1,748
651
United States
It is not too simplistic because the machines act independently. It is that independence that permits, indeed requires, using a simple additive function.
 
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Oct 2010
58
3
Sorry for the late reply, but thanks a lot for the confirmation!
 
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