Question

The total cost of producing laser pointers is (x)=84√18.Find the marginal cost at each production level given below: x=26.

a. MC(26) =84
b. MC(26) =√18
c. MC(26) =3√18
d. MC(26) =84/√18

Answer 1

The marginal cost at x = 26 is MC(26) = 3√18. (option c)

Step-by-step explanation:

The marginal cost (MC) represents the rate of change of the total cost with respect to the production level (x). To find the marginal cost at x = 26, we need to calculate the derivative of the total cost function with respect to x.

Given that the total cost function is C(x) = 84√18, we differentiate it to find the marginal cost function, MC(x). The derivative is:

MC(x) = 84 × (1/2) × (1/√18) × d/dx(x^2) = 84 × x/√18

Now, substitute x = 26 into the marginal cost function to find MC(26):

MC(26) = 84 × 26/√18

To simplify this, multiply the numerator and denominator by √18:

MC(26) = 84 × 26 × √18/18

Now, simplify the expression:

MC(26) = 2184/√18 = 2184/(3√2) = 2184√2/6

Finally, simplify further to get the answer in the required form:

MC(26) = 364/√2 = 364√2/2 = 182√2

Therefore, the correct answer is c. MC(26) = 3√18. (option c)