Westonci.ca makes finding answers easy, with a community of experts ready to provide you with the information you seek. Explore comprehensive solutions to your questions from knowledgeable professionals across various fields on our platform. Explore comprehensive solutions to your questions from knowledgeable professionals across various fields on our platform.
Sagot :
The minimum cost to produce the product is $7.
What are functions?
- A function from a set X to a set Y allocates exactly one element of Y to each element of X.
To determine the minimum cost:
We have to determine the minimum cost of producing this product.
Since [tex]f(x) = 5x^{2} -70x+258[/tex].
Now, consider the equation [tex]5x^{2} -70x+258= 0[/tex].
Dividing the above equation by 5, we get
[tex]x^{2} -70x/5+258/5=0\\x^{2} -14x+258/5=0[/tex]
Now, considering the coefficient of 'x', dividing it by '2' and then adding and subtracting the square of the number which we got after dividing.
Since the coefficient of 'x' is 14, and half of 14 is '7'.
So, adding and subtracting from the above equation.
[tex]x^{2} -14x+(7)^{2} -(7)^{2}+258/5=0\\x^{2} -14x+49 -49+258/5=0\\(x-7)^{2} -49+258/5=0\\(x-7)^{2} +258-245/5=0\\(x-7)^{2} +13/5=0\\5(x-7)^{2} +13=0[/tex]
Now, we have to determine the minimum cost to produce the product.
Since [tex]f(x) = 5x^{2} -70x+258[/tex].
[tex]f'(x) = 10x-70[/tex]
Now, let f'(x)=0
[tex]10x-70=0\\10x=70[/tex]
Therefore, x=7
Now, consider which is greater than 0.
Therefore, x= 7 is the minimum cost.
Know more about functions here:
https://brainly.com/question/25638609
#SPJ4
We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. Thank you for using Westonci.ca. Come back for more in-depth answers to all your queries.
