Let's say a company manages two types of projects A and B. A type projects are more complex than B type projects. A study found that the ideally, a project manager can handle at the same time 2 type A projects and 7 type B projects. There are currently 300 type A projects and 700 type B projects. How many project managers are needed to manage these projects while respecting the ideal number of A & B projects per project manager?
I'm trying to come up with the equation but can't seem to get it right....
Unless you have some information on how the number of A projects one manager can handle varies depending on the number of B projects, the best you can do is assign each manager 2 A's and 7 B's. Then you need 150 project managers to staff the A's and they get off easy because there aren't enough B's to go around. But if you knew that one manager could also handle (for example) 3A's and 4B's you could try to find a mix that reduced the number. We would say there were $a$ of the first kind and $b$ of the second and say $2a+3b=300, 7a+4b=700$ and solve that (rounding up) to give $\frac {13}3a=300, a=\frac {900}{13}=70, b=\frac {210}{4}=53$, for a total of $123$