Respuesta :
We have a cost function that express the cost of producing x golf clubs per day:
[tex]C(x)=550+130x-0.9x^2[/tex]A) We have to to find the marginal cost. The marginal cost at a certain level of production x represents the cost of producing one more unit.
It can be calculated as the first derivative of the cost function:
[tex]\begin{gathered} C^{\prime}(x)=550(0)+130(1)-0.9(2x) \\ C^{\prime}(x)=130-1.8x \end{gathered}[/tex]B) In this case, we have to calculate the marginal cost when the level of production is 55 golf clubs (x = 55):
[tex]\begin{gathered} C^{\prime}(55)=130-1.8(55) \\ C^{\prime}(55)=130-99 \\ C^{\prime}(55)=31 \end{gathered}[/tex]Answer:
A) C'(x) = 130 - 1.8x
B) C'(55) = 31
