question 15 (multiple choice worth 1 points) (08.05 mc) the following function represents the production…

question 15 (multiple choice worth 1 points) (08.05 mc) the following function represents the production cost f(x), in dollars, for x number of units produced by company 1: f(x)=0.05x^2 - 7x + 300 the following table represents the production cost g(x), in dollars, for x number of units produced by company 2: x g(x) 0.6 899.58 0.8 899.52 1 899.50 1.2 899.52 1.4 899.58 based on the given information, determine which company has a lower minimum and find the minimum value. f(x) at (1, 899.50) g(x) at (70, 55) f(x) at (70, 55) g(x) at (1, 899.50)

question 15 (multiple choice worth 1 points) (08.05 mc) the following function represents the production cost f(x), in dollars, for x number of units produced by company 1: f(x)=0.05x^2 - 7x + 300 the following table represents the production cost g(x), in dollars, for x number of units produced by company 2: x g(x) 0.6 899.58 0.8 899.52 1 899.50 1.2 899.52 1.4 899.58 based on the given information, determine which company has a lower minimum and find the minimum value. f(x) at (1, 899.50) g(x) at (70, 55) f(x) at (70, 55) g(x) at (1, 899.50)

Answer

Explanation:

Step1: Find the minimum of $f(x)$

For a quadratic function $y = ax^{2}+bx + c$ ($a\neq0$), the x - coordinate of the vertex (which is the minimum or maximum) is given by $x=-\frac{b}{2a}$. For $f(x)=0.05x^{2}-7x + 300$, where $a = 0.05$, $b=-7$, and $c = 300$. Then $x=-\frac{-7}{2\times0.05}=\frac{7}{0.1}=70$. Substitute $x = 70$ into $f(x)$: $f(70)=0.05\times(70)^{2}-7\times70 + 300=0.05\times4900-490 + 300=245-490+300 = 55$.

Step2: Analyze $g(x)$ from the table

From the table of $g(x)$, the minimum value of $g(x)$ in the given data points is $g(1)=899.50$.

Step3: Compare the minimums

Since $55<899.50$, $f(x)$ has a lower minimum. The minimum value of $f(x)$ is 55 when $x = 70$.

Answer:

$f(x)$ at $(70,55)$