Math question help?

Another company sells wrought iron umbrella trees. This company has fixed costs of $100,000/month. The cost in labor and material is $15 per umbrella sold per month. To sell x items, the price must be set at $50-0.5x, where x is in thousands of umbrellas sold per month. What price will maximize profit?

Math question help?
profit (P) = income (I) - cost (C)


P = (50-0.5x)x - (100,000 + 15x)


P' = 50 - x - 15


Solve P' = 0 for x,


x = 35


Price = 50-0.5*35 = $32.5
Reply:Costs are: 100000+15X, where X is umbrellas.


Sales are: X(50-0.5*X/1000)


Profit is: 50X - 0.0005 * X^2 - 100000-15 X


-0.0005*X^2 + 35 X - 100000.


Now take the derivitive of this,, set it equal to zero and determine X. Then determine the price at this value of X.

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