Final answer:
To find the marginal cost at a production level of x golf clubs, calculate the first derivative of the total cost function G(x) = 800 + 90x - 0.1x², which gives C'(x) = 90 - 0.2x. Then, evaluate this derivative at the specific production level to obtain the marginal cost in dollars per additional golf club produced.
Step-by-step explanation:
The student is asking how to find the marginal cost at a certain production level for producing golf clubs, given a specific cost function. The marginal cost can be found by calculating the first derivative of the total cost function with respect to the quantity of golf clubs, and then evaluating this derivative at the given production level.
The total cost function given is G(x) = 800 + 90x - 0.1x². To find the marginal cost function, C'(x), we take the derivative of G(x) with respect to x, which yields C'(x) = 90 - 0.2x. So, the marginal cost at a production level of x golf clubs is 90 - 0.2x dollars per golf club. For example, if we want to find the marginal cost at a production level of 40 golf clubs, we would substitute x = 40 into the marginal cost function to find C'(40) = 90 - (0.2*40) = 82 dollars per additional golf club.