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) = -0.1x^2 + 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

Answer:

Option D

Step-by-step explanation:

Let the manufacturing unit operates with the maximum capacity = x

Since manufacturing unit currently operates at 80%

So function f(x) that models the current capacity of the unit will be

f(x) = (0.80)x

Given profit function for the unit at optimum output is

p(x) = ( -0.1) x² + 80x - 60

so composite function giving the unit's current profit function will be

p[f(x)] = (-0.1) (0.8x)² + 80(0.80x) - 60

         = -(0.1) (0.64x²) + 80 (0.08x) - 60

         = - 0.64x² + 6.4x - 60

Option D will be the answer.

Answer 2

B.
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