Question

The toal cost (in dollars) of producing x golf clubs per day is given by the formula C(x)=752+90x−0.8r²

(A) Find the marginal cost equation 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 =

Answer 1

To find the marginal cost equation, take the derivative of the total cost function with respect to production level. The marginal cost equation is MC(x) = 90 - 1.6x. To find the marginal cost of producing 35 golf clubs, substitute x = 35 into the marginal cost equation.

Step-by-step explanation:

To find the marginal cost equation, we need to calculate the derivative of the total cost function with respect to the production level (x). We can do this by taking the derivative of each term separately. Using the formula C(x) = 752 + 90x - 0.8x², the marginal cost equation is found by taking the derivative of each term:

• Marginal cost = derivative of 752 + derivative of 90x + derivative of -0.8x²
• Marginal cost = 0 + 90 + (-0.8 * 2x)
• Marginal cost = 90 - 1.6x

So, the marginal cost equation is given by MC(x) = 90 - 1.6x.

To find the marginal cost of producing 35 golf clubs, plug x = 35 into the marginal cost equation:

• Marginal cost for 35 clubs = 90 - 1.6 * 35
• Marginal cost for 35 clubs = 90 - 56
• Marginal cost for 35 clubs = 34