formula help?

[Jeffy]

WHERE CAN I FIND A FORMULA FOR THIS?

The annual revenue and cost functions for a manufacturer of grandfather clocks are approximately R(x) = 480x - 0.01x^2 and C(x) = 200x + 100,000 , where x denotes the number of clocks made. What is the maximum annual profit?


WHEN I DID IT MY WAY I GOT $2,160,000 but I am sure I did it wrong since I am not too good at calc.

 

[skeeter]

profit = revenue - cost

P(x) = (480x - .01x^2) - (200x + 100000)

P(x) = -.01x^2 + 280x - 100000

P'(x) = -.02x + 280

set P'(x) = 0

-.02x + 280 = 0

x = 14000

since the graph of P(x) is a concave down parabola, max profit occurs when
x = 14000 units

P(14000) = 1,860,000