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The production cost C of n units of a product is calculated:

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Senior Manager
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New post 23 May 2007, 09:17
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The production cost C of n units of a product is calculated: C=1000+100*n-n^2, where n<50. The revenue R = N*(400-16*n). Find n if the profit P (P=R-C) is maximum.
A) 20
B) 30
C) 49
D) 16
E) 10
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New post 23 May 2007, 09:39
Answer: E

P=R-C=-15n^2+300n-1000 Since this equation is quadratic it gets its MAX value when n=-(b/2a)

n=-(300/2*(-15))=10

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New post 23 May 2007, 10:02
I agree with UMB. This is a parabola (a quadratic expression). We know that its vertex is the highest point because the number in front of x^2 is negative. -b/2a gives you the value of the vertex.
  [#permalink] 23 May 2007, 10:02
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The production cost C of n units of a product is calculated:

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