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**Macleef** A special CD is manufactured and its manufacturing costs is given by the equation C(x) = 0.08x^2 + 0.2x + 3200. If the price function is given by the equation p(x) = 33 - 0.02x, determine the price that should be charged

a) to maximize profits

$\displaystyle P(x) = R(x) - C(x)$

$\displaystyle R(x) = \frac {33 - 0.02x} {x}$

$\displaystyle R(x) = \frac {33}{x} - 0.02$

$\displaystyle P(x) = \frac {33}{x} - 0.02 - 0.08x^2 - 0.2x - 3200$

$\displaystyle P(x) = \frac {33}{x} -3200.02 - 0.2x - 0.08x^2$

$\displaystyle P'(x) = \frac {33}{x^2} -3200.02 - 0.2x - 0.08x^2$

$\displaystyle 0 = \frac {33}{x^2} -3200.02 - 0.2x - 0.08x^2$

$\displaystyle 3200.02 = \frac {33}{x^2} - 0.2x - 0.08x^2$

$\displaystyle 3200.02 = \frac {33 - 0.2x^{3} - 0.008^{4}}{x^2}$

$\displaystyle 3200.02x^2 = 33 - 0.2x^{3} - 0.008^{4}$

$\displaystyle 3200.02x^2 = 33 - 0.2x^{3} - 0.008^{4}$

Now I don't know what to do. . .? I can't seem to find the zeros of the first derivative. . .