Question

You have a factory that manufactures something that is at least somewhat complicated. The cost in dollars of manufacturing x items is given by the function y = C(x).
(a) Make a realistic sketch for the graph of C. You don’t have to label the axes because you don’t have any idea what the cost of any of the items are. Explain why you made the graph the way you did. Include in your discussion your choice for y intercept (was it positive, negative, or zero?), whether the function is linear or not, whether it is increasing for.Explain what the expression C(150) − C(100) over (150-100) represents.

Answer 1

That's what I have so far, unfortunately I don't understand what the equation means. \[C(150)-C(100) \over 150-100\]

Answer 2

\[\frac{C(150)-C(100)}{150-100}\]
This expression represents the average manufacturing cost per item for quantities between 100 items and 150 items

Answer 3

If I were to plot the points x=100 and x=150 would x=100 be the midpoints of their concave areas?

Answer 4

According to the question it does not appear possible to plot points.
Considering your graph of C the positive slope will reduce with increased production quantities. However I don't agree with the point of inflexion in your graph at the upper end. There will always be fixed production costs per item that ensure the slope will not become negative at the higher production quantities.