SOLUTION: Marginal cost can be thought of as the cost of producing one additional unit of output. the marginal cost C (in dollars) to produce x bicycles is C(x)x^2-40x+530 (C)economic

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Question 1058124: Marginal cost can be thought of as the cost of producing one additional unit of output. the marginal cost C (in dollars) to produce x bicycles
is C(x)x^2-40x+530
(C)economic theory states that, to maximize profit, production should continue until marginal revenue equals marginal cost. assuming that marginal revenue equals $230, how much bicycles should be manufactured ?

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+230+=+C%28x%29+
+230+=+x%5E2++-+40x+%2B+530+
+x%5E2+-+40x+=+-300+
Complete the square
+x%5E2+-+40x+%2B+%2840%2F2%29%5E2+=+-300+%2B+%2840%2F2%29%5E2+
+x%5E2+-+40x+%2B+400++=+-300+%2B+400+
+%28+x+-+20+%29%5E2+=+100+
Take the square root of both sides
+x+-+20+=+10+
+x+=+30+
and, taking the negative square root of +100+,
+x+-+20+=+-10+
+x+=+10+
This says either +x+=+10+ or +x+=+30+ works
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Here's the plot:
+graph%28+400%2C+400%2C+-10%2C+50%2C+-100%2C+500%2C+x%5E2+-+40x+%2B+300+%29+