The total cost (in dollars) of producing x golf clubs per day is given by the formula
C(x)=500+100x−0.1x2.
(A) Find the marginal cost at a production level of x golf clubs.
C′(x) =
(B) Find the marginal cost of producing 35 golf clubs.
Marginal cost for 35 clubs =
you have the functions. Just plug in the values.
dC/dx = 100 - .2 x
at x = 35
dC/dx = 100 - 7 = 93 dollars per club at a level of 35 clubs
by the way total C for 35 clubs = 3877.5 or about an average of 111 dollars per club
(A) To find the marginal cost at a production level of x golf clubs, we need to take the derivative of the cost function C(x) with respect to x.
C(x) = 500 + 100x - 0.1x^2
Taking the derivative of C(x), we have:
C'(x) = 100 - 0.2x
Therefore, the marginal cost at a production level of x golf clubs is C'(x) = 100 - 0.2x.
(B) To find the marginal cost of producing 35 golf clubs, we can substitute x = 35 into the marginal cost function C'(x):
C'(35) = 100 - 0.2(35)
C'(35) = 100 - 7
C'(35) = 93
Therefore, the marginal cost of producing 35 golf clubs is 93 dollars.
To find the marginal cost, we need to take the derivative of the cost function with respect to x.
(A) Finding C'(x):
The given cost function is C(x) = 500 + 100x - 0.1x^2.
To find C'(x), we need to differentiate the function with respect to x. The derivative of each term is as follows:
d(500)/dx = 0 (since 500 is a constant)
d(100x)/dx = 100 (since the derivative of x is 1)
d(-0.1x^2)/dx = -0.2x (using the power rule, where the derivative of x^n is nx^(n-1))
Taking the derivatives of each term, we have:
C'(x) = 0 + 100 - 0.2x
Simplifying this expression, we get:
C'(x) = 100 - 0.2x
(B) Finding the marginal cost for producing 35 golf clubs:
To find the marginal cost for producing 35 golf clubs, we substitute x = 35 into the derivative that we found in part (A).
C'(x) = 100 - 0.2x
Substituting x = 35:
C'(35) = 100 - 0.2(35)
C'(35) = 100 - 7
C'(35) = 93
Therefore, the marginal cost of producing 35 golf clubs is 93 dollars.