3. A company's profit function at a given level of output, x, is expressed as: P(x) = -0.001x2 + 8x - 5,000 What level of output will maximize profit?...

3.A company’s profit function at a given level of output, x, is expressed as: P(x) = -0.001x2 + 8x – 5,000What level of output will maximize profit? How much profit will be earned at that level of output? $

P(x) = -0.001x2 + 8x – 5,000 Finding maxima by Differentiating P(x) with respect to xdP(x)/dx = -0.001(2x) + 8Now, Putting dP(x)/dx = 0,-0.001(2x) + 8 = 00.002x = 8x = 4000Therefore, an...