Question

23. A manufacturer is in the business of producing small models of the Statue of Liberty. He finds that the daily cost in dollars, C, of ​​producing n statues is given by the quadratic formula C=n^2 - 120 + 4200. How many statues should be produced per day so that the cost will be minimum? What is the minimal daily cost?

Answer 1

we are given that :

cost in dollars, C, of ​​producing n statues is given by the quadratic formula$\\\C=n^2 - 120n + 4200$

The minimum cost will be at the x-coordinate of the vertex of the parabola represented by the given equation.

Compare with the standard equation

$\\\ ax^2+bx+c=0$

we get a=1, b= -120

X-coordinate of the vertex$\\\=\frac{-b}{2a}=-\frac{-120}{2*1}=60$

Hence 60 statue should be produced daily to minimize the cost.

Minimum daily cost=60^2 - 120*60 + 4200=$600

Answer 2

we are given that :

cost in dollars, C, of ​​producing n statues is given by the quadratic formula \\\C=n^2 - 120n + 4200\\

The minimum cost will be at the x-coordinate of the vertex of the parabola represented by the given equation.

Compare with the standard equation

\\\ ax^2+bx+c=0\\

we get a=1, b= -120

X-coordinate of the vertex \\\=\frac{-b}{2a}=-\frac{-120}{2*1}=60\\

Hence 60 statue should be produced daily to minimize the cost.

Minimum daily cost=60^2 - 120*60 + 4200=$600

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