Question

The total cost (in dollars) of producing 2 golf clubs per day is given by the formulaC(x) = 550 + 130x - 0.9x^2.(A) Find the marginal cost at a production level of a golf clubs.C' (x) =(B) Find the marginal cost of producing 55 golf clubs.Marginal cost for 55 clubs =

Answer 1

Given the total cost function:

`C(x)=550+130x-0.9x^2`

(a)

The marginal cost is the derivative of the cost function. Then, taking the derivative of C(x):

`\begin{gathered} C^(\prime)(x)=0+130\cdot1-0.9\cdot2\cdot x \\ \Rightarrow C^(\prime)(x)=130-1.8x \end{gathered}`

(b)

The marginal cost of producing 55 golf clubs (x = 55 in the previous function):

`\begin{gathered} C^(\prime)(55)=130-1.8\cdot55 \\ \Rightarrow C^(\prime)(55)=\text{ \$}31 \end{gathered}`