Linear Equations In One Variable

The variable cost,

VC(x)

, of producing

x

dolls is given by

VC(x)%20%3D%203x%5E2

. The fixed cost for packaging

x

dolls is

%E2%82%B92800

. Therefore, the total cost

TC(x)

is:

TC(x)%20%3D%20VC(x)%20%2B%20%5Ctext%7BFixed%20Cost%7D%20%3D%203x%5E2%20%2B%202800

The marginal cost is the derivative of the total cost with respect to

x

, denoted by

MC(x)

. Thus, find the derivative

TC'(x)

%5Cfrac%7Bd%7D%7Bdx%7D(3x%5E2%20%2B%202800)%20%3D%206x

To find the marginal cost of producing 120 dolls, substitute

x%20%3D%20120

into the derivative:

MC(120)%20%3D%206%20%5Ctimes%20120%20%3D%20720

Thus, the marginal cost of producing 120 dolls is

%E2%82%B9720

Chapter Questions
1 MCQs