Question

Question 7(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) = 0.15x2 − 6x + 400

The following table represents the production cost g(x), in dollars, for x number of units produced by company 2:


x g(x)
50 75
60 60
70 55
80 60
90 75


Based on the given information, determine which company has a lower minimum and find the minimum value.
g(x) at (70, 55)
f(x) at (20, 340)
f(x) at (70, 55)
g(x) at (20, 340)

Answer 1

A, I took the test and got it right

Explanation:

Answer 2

Option A.

Explanation:

The given function is

`f(x)=0.15x^2-6x+400`

Leading coefficient is positive, so it is an upward parabola. Vertex of an upward parabola is the point of minima.

Vertex of a parabola
`f(x)=ax^2+bx+c` is

`Vertex=\left((-b)/(2a),f((-b)/(2a))\right)`

In the given function a=0.15, b=-6 and x=400.

`-(b)/(2a)=-(-6)/(2(0.15))=20`

At x=20,

`f(20)=0.15(20)^2-6(20)+400=340`

So, minimum value of f(x) is 340 at x=20.

From the given table it is clear that the minimum value of g(x) is 55 at x=70.

Since 55 < 340, therefore, g(x) has a lower minimum values, i.e, (70,55).

Hence, option A is correct.