Question 1039082: The cost, in dollars, for a company to produce x widgets is given by C(x) = 3600 + 5x for x greater than or equal to 0, and the price-demand function, in dollars per widget, is p(x) = 45 - .04x for 0 less than or equal to x less than or equal to 1125.
(a) The profit function is a quadratic function and so its graph is a parabola.
Does the parabola open up or down? __________
(b) Find the vertex of the profit function P(x) using algebra. Show algebraic work please.
I would really appreciate your help on this!
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! The cost, in dollars, for a company to produce x widgets is given by C(x) = 3600 + 5x for x greater than or equal to 0, and the price-demand function, in dollars per widget, is p(x) = 45 - .04x for 0 less than or equal to x less than or equal to 1125.
(a) The profit function is a quadratic function and so its graph is a parabola.
Does the parabola up or down? __________
Cost:: C(x) = 3600+5x
Revenue:: (unit price)*(# of units) = x(45-0.04x) = 45x-0.04x^2
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Profit = Revenue - Cost = 45x-0.04x^2 - (3600+5x) = -0.04x^2 +40x - 3600
Ans: Opens down because the coefficient of x^2 is negative
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(b) Find the vertex of the profit function P(x) using algebra. Show algebraic work please.
Vertex occurs where x = -b/(2a) = -40/(2*-0.04) = -40/(-0.08)= 4000/8 = 500
f(500) = -0.04*500^2 + 40*500 - 3500 = 6500
Ans:: vertex :: (500,6500)
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Cheers,
Stan H.
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