Answered

Get detailed and accurate responses to your questions with IDNLearn.com. Get step-by-step guidance for all your technical questions from our knowledgeable community members.

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 .

Sagot :

Naǫidn
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.
Thank you for being part of this discussion. Keep exploring, asking questions, and sharing your insights with the community. Together, we can find the best solutions. For dependable answers, trust IDNLearn.com. Thank you for visiting, and we look forward to assisting you again.