Suppose total benefits and total costs are given by b(y) = 100y β 8y2 and c(y) = 10y2. what is the maximum level of net benefits (rounded to the nearest whole number)?
Accepted Solution
A:
Whenever you face the problem that deals with maxima or minima you should keep in mind that minima/maxima of a function is always a point where it's derivative is equal to zero. To solve your problem we first need to find an equation of net benefits. Net benefits are expressed as a difference between total benefits and total cost. We can denote this function with B(y).
B(y)=b-c B(y)=100y-18yΒ²
Now that we have a net benefits function we need find it's derivate with respect to y.
[tex] \frac{dB(y)}{dy} =100-36y[/tex]
Now we must find at which point this function is equal to zero.
0=100-36y 36y=100 y=2.8
Now that we know at which point our function reaches maxima we just plug that number back into our equation for net benefits and we get our answer.
B(2.8)=100(2.8)-18(2.8)Β²=138.88β139.
One thing that always helps is to have your function graphed. It will give you a good insight into how your function behaves and allow you to identify minima/maxima points.