A new small toy has the following price-demand relation: p=60x ^-1/2 where \"p\"

Question

A new small toy has the following price-demand relation: p=60x ^-1/2 where "p" represents price in dollars and "x" represents demand per week. The weekly total cost of producing this new toy is: C(x)=0.40x+800 a) Find the Revenue function for this new toy. b) Find the Profit function for this new toy. c) What quantity of this new toy should be produced and sold weekly to maximize profit? Show all work. d) What is the maximum possible amount of weekly Profit for this new small toy? e) At what selling price is the weekly Profit optimized?

Explanation / Answer

a)revenue function=p*x=60x^2-1/2x b)Profit function=60x^2-1/2x-0.4x^2-800x= 59.6x^2-800.5x c)x=7 d)$2683

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