Question

1. the average cost for a company to produce x items is $x^2 - 10x + 43$ dollars. how many items should the company produce to minimize the average cost per item?

options: 10, 18, 5, 43

Explanation:

Step1: Identify the function type

The average cost function is \( C(x)=x^{2}-10x + 43 \), which is a quadratic function in the form \( y = ax^{2}+bx + c \) where \( a = 1 \), \( b=- 10 \), \( c = 43 \).

Step2: Find the vertex of the parabola

For a quadratic function \( y=ax^{2}+bx + c \), the x - coordinate of the vertex (which gives the minimum value when \( a>0 \)) is given by the formula \( x=-\frac{b}{2a} \).

Substitute \( a = 1 \) and \( b=-10 \) into the formula:
\( x=-\frac{- 10}{2\times1}=\frac{10}{2} = 5 \)

So the company should produce 5 items to minimize the average cost per item.

Answer:

5