User5890
Consider an office of 45 employees, whose average age is 40 years. ‘x’ new employees join this office, whose average age is ‘y’ years. If it is known that×+y=50,thenwhatcanbethe maximum possible average age of all the employees now?
Let’s take the average age of all the guys, which is (a+b+c+..+d)/45=40. Another is (m+n+...+l)/x=y, where x+y=50 and y=50-x.
Average ages for everyone may be (a+b+c+..+d+m+n+..+l)/(45+x)=>; what is the maximum for that?
[-x2+50x+1800]/(45+x)=> (45*40+x*y)/(45*40+x*(50-x))/(45+x)=(45*40+x*(50-x)) To determine this function’s maximum value, we can utilize the derivative in this case. If we do, it would look something like this: [(-2x+50)*(45+x)-(-x26+50x+1800)]/(45+x)2=0 -x2-90x+450=0 x1=5 (about 4.8), x2=-95, for here we will take 5 since we need a greater value. When we use the previous function, [-x2+50x+1800]/(45+x), the result could be 40.5 or so.)