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a manufacture of brand A jeans has daily production costs of C =0.2x^2 -96x+12,095 where C is the total cost in dollars and x is the number of jeans produced. How many jeans should be produced each day in order to minimize costs? what is the minimum daily cost .

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The minimum of the function is at the vertex of the parabola represented by the equation.
The x-coordinates is the number of jeans that should be produced in order to minimize costs.
The y-coordinate is the minimum cost.

[tex]C(x)=0.2x^2-96x+12095 \\ a=0.2 \\ b=-96[/tex]

The vertex of a parabola is (h,k), where:
[tex]h=\frac{-b}{2a}=\frac{-(-96)}{2 \times 0.2}=\frac{96}{0.4}=240 \\ \\ k=C(h)=C(240)=0.2 \times 240^2-96 \times 240+12095= \\ =11520-23040+12095=575[/tex]

240 jeans should be produced each day in order to minimize costs. The minimum daily cost is $575.
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