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 . If the optimum output is 500 units, the current profit is $.

The profit function is -0.1x² + 80x - 60

To account for 80% capacity, we substitute f(x) = .8x for every x in the equation:
p(f(x)) = -.1(.8x)^2 + 80(0.8x) - 60
p(f(x)) = -0.064x² + 64x - 60

Plugging in 500 for x:
p(f(500)) = -0.064 (500²) + 64 (500) -60
p(f(500)) = 15940