vdemidoff wrote:All of the 200 engineers who work at a software company are to be assigned to work on either new product development or maintenance of old products. At least 60 percent of them request to work on new product development. If at least 65 percent of engineers are to be assigned to maintenance of old products, what is the least number of engineers who will not get their requested [/color]assignment?[/color]
HELP!!!!!!!!!!!
Hi vdemidoff,
let's pretend there are 100 and not 200 engineers. We'll just have to be sure to remember to double our final answer.
There are two categories:
Product Development (PD)
Maintenance of Old Products (MO)
We have to MINIMIZE the number of engineers who get an assignment they did not request. That is the task.
At least 65 (of our 100) have to be assigned to MO.
But at least 60 of them requested PD; therefore, at most 40 did NOT request PD.
These 40, who did not request PD, can all go to MO. Then MO still needs 25 enginners assigned to it. We will have to draw these 25 from the (sixty) who requested PD.
Therefore, at least 25 will get an assignement they did not request.
We have to double this (remember there are 200 and not 100), so there will be at least 50 engineers who will get an assignment they did not request.
Because we had to find the least number of engineers who would get an assignment they did not request, we wanted to a) minimize the number who DID request an assignment (or maximize the number who didn't) and b) minimize the number of necessary assignments to MO.
