Answer:
The minimum cost of producing this product is:
13
Step-by-step explanation:
The function which is used to represent the cost to produce x elements is given by:
[tex]f(x)=5x^2-70x+258[/tex]
Now, on simplifying this term we have:
[tex]f(x)=5(x^2-14x)+258\\\\i.e.\\\\f(x)=5(x^2+49-49-14x)+258\\\\i.e.\\\\f(x)=5((x-7)^2-49)+258\\\\i.e.\\\\f(x)=5(x-7)^2-5\times 49+258\\\\i.e.\\\\f(x)=5(x-7)^2-245+258\\\\i.e.\\\\f(x)=5(x-7)^2+13[/tex]
We know that:
[tex](x-7)^2\geq 0\\\\i.e.\\\\5(x-7)^2\geq 0\\\\i.e.\\\\5(x-7)^2+13\geq 13[/tex]
This means that:
[tex]f(x)\geq 13[/tex]
This means that the minimum cost of producing this product is: 13
