For a small manufacturing firm the unit cost Cx in dollars o

For a small manufacturing firm, the unit cost C(x) in dollars of producing x units per day is given by

C(x) = x² 40x + 5500.

How many items should be produced per day to minimize the unit cost?


What is the minimum unit cost?
$

Solution

C(x)=x²-40x+5500

The cost is minimum at minimum value of x and x is minimum at the vertex which is ,x=-(-40)/(2)=20

And minimum cost is c(x)=(20²)-40(20)+5500 =5100