a production company determined the average cost of employing each employee and then created the forecast to determine their net profit (gross profit minus the cost of x employees)
in the graph below f(x) is the net profit, n=32, m=64 and p=$339,968
during which interval are the employee cost greater than the company earnings?
To find the interval during which the employee cost is greater than the company earnings, we need to compare the net profit function f(x) with 0 (company earnings).
Given that f(x) = 339,968 - (32x + 64(64-x)) = 339,968 - (-32x + 64*64) = 339,968 + 32x - 4096 = 32x - 505580
We want to find the interval where f(x) < 0
Solving for x:
32x - 505580 < 0
32x < 505580
x < 505580 / 32
x < 15232.8125
Therefore, the employee cost is greater than the company earnings when x < 15232.8125, or in the interval x < 15232.