Friday, November 13, 2009

Calculus problem:?

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 $50-0.3x, where x is in thousands of umbrellas sold per month. What price will maximize profit?


price=_______________

Calculus problem:?
price = $32.50
Reply:Cost = 100,000 +15x


Revenue = (50- .3x)x


Profit = (50-.3x)x - 100000+15x


P = 50x-.3x^2 -100000+15x


P = -.3x^2 +50x -100000


dP/dx = -.6x +50


.6x+ 50


x = 50/.6 = 83.3


Price = 50- 83.33*.3 = 25$


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