The function c (p) represents the total cost for a factory to produce p parts. c (p) = 12.5p+4500 What does the value 4500 represent in this situation?

The function works as follows:

If, for example, we want to produce 100 parts, the total cost is calculated as follows:

c (100) = 12.5*100+4,500=1,250+4,500=5,750 (dollars, or some other unit).

We note that if p=0 (that is, if no parts are produced) then

p (0) = 12.5*0+4,500=0+4,500=4,500.

Thus, 4,500 represents the initial costs, without producing any part.