Question

The cost to produce a product is modeled by the function f(x) = 5x2 − 70x + 258 where x is the number of products produced. Complete the square to determine the minimum cost of producing this product. 5(x − 7)2 + 13; The minimum cost to produce the product is $13. 5(x − 7)2 + 13; The minimum cost to produce the product is $7. 5(x − 7)2 + 258; The minimum cost to produce the product is $7. 5(x − 7)2 + 258; The minimum cost to produce the product is $258.

Answer 1

The cost to produce a product is modeled by the function $f(x)=5x^{2}-70x+258$ , where x is the number of products produced.

We have to determine the minimum cost of producing this product.

Since, $f(x)=5x^{2}-70x+258$

Now, consider the equation $5x^{2}-70x+258=0$

Dividing the above equation by 5, we get

$x^{2}-\frac{70x}{5}+\frac{258}{5}=0$

$x^{2}-14x+\frac{258}{5}=0$

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, coefficient of 'x' is 14, and half of 14 is '7'.

So, adding and subtracting $7^{2}$ from the above equation.

$x^{2}-14x+(7)^{2}-(7)^{2}+\frac{258}{5}=0$

$x^{2}-14x+49-49+\frac{258}{5}=0$

$(x-7)^{2}-49+\frac{258}{5}=0$

$(x-7)^{2}+\frac{258-245}{5}=0$

$(x-7)^{2}+\frac{13}{5}=0$

$5(x-7)^{2}+13=0$

Now, we have to determine the minimum cost to produce the product.

Since, $f(x)=5x^{2}-70x+258$

$f'(x)=10x-70$

Now, let f'(x)=0

$10x-70=0$

$10x=70$

Therefore, x=7

Now, consider $f''(x)=10$ which is greater than 0.

Therefore, x= 7 is the minimum cost.

The minimum cost to produce the product is $7.

Answer 2

Answer:

The answer is “A”

Step-by-step explanation:

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