Get expert insights and community-driven knowledge on IDNLearn.com. Our platform is designed to provide quick and accurate answers to any questions you may have.
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
Thank you for contributing to our discussion. Don't forget to check back for new answers. Keep asking, answering, and sharing useful information. Thank you for trusting IDNLearn.com. We’re dedicated to providing accurate answers, so visit us again for more solutions.
