Question

A manufacturing unit currently operates at 80 percent of its capacity. The profit function for the unit at the optimum output, x, is given by p(x) = -0.1x2 + 80x − 60. If the function f(x) models the current capacity of the unit, the composite function giving the unit's current profit function is

a.f(p(x))=-0.064x^2+6.4x-60
b.p(f(x))=-0.64x^2+0.64x-60
c.p(f(x))=-0.064x^2+64x-60
d.p(f(x))=-0.64x^2+6.4x-60
e.f(p(x))=-0.064x^2+64x-60
If the optimum output is 500 units, the current profit is $a.15,400 b.15,940 c.16,060 d.16,600

Answer 1

What are you doing with this equation?

Answer 2

the output is being reduced to 80% of its optimum output so f(x) = 0.80x

plug this in for x into the profit function to find the composite function

then for the second part, plug in optimum = x = 500 units to get the profit function

Answer 3

Thanks!