The average income, i, in dollars, of a lawyer with an age of x years is modeled with the following function: i = -425x^2 + 45,500x – 650,000. what is the youngest age for which the average income of a lawyer is $275,000? round to the nearest year. according to this model, what is the predicted average annual income of 40-year-old lawyers? round to the nearest whole dollar.

We are given

The average income, I, in dollars is

(a)

now, we are given

average income is $275000

so,

now, we can set them equal

and then we can solve for x

we will have to use quadratic formula

we get

we need to find youngest age

It means that we need to choose smallest value

so,

............Answer

(b)

we are given

x=40

so, we can plug it and find I

..............Answer

answer: evaluate the objective function at each vertex to determine which - and -values, if any, maximize or minimize the function. example: find the minimum value and maximum value of the objective function f ( x , y ) = 4 x + 5 y , subject to the following constraints