Question

For the given cost function C(x) = 54√x + (x²/91125), find a) The cost at the production level 2000, b) The average cost at the production level 2000, and c) The marginal cost at the production level 2000.

Answer 1

The cost at the production level 2000 is $2455.50. The average cost at the production level 2000 is $1.23. The marginal cost at the production level 2000 is $0.649.

Step-by-step explanation:

a) The cost at the production level 2000:

To find the cost at the production level 2000, we need to substitute x=2000 into the given cost function C(x).

C(2000) = 54√2000 + (2000²/91125)

C(2000) = 54(44.72) + (2000²/91125)

C(2000) = 2411.68 + 43.82

C(2000) = 2455.50

The cost at the production level 2000 is $2455.50.

b) The average cost at the production level 2000:

The average cost can be found by dividing the total cost at the production level 2000 by the production level 2000.

Average Cost = Total Cost / Production Level

Average Cost = $2455.50 / 2000

Average Cost = $1.23

The average cost at the production level 2000 is $1.23.

c) The marginal cost at the production level 2000:

The marginal cost can be found by taking the derivative of the cost function with respect to x, and then substituting x=2000.

C'(x) = (54/2√x) + (2x/91125)

C'(2000) = (54/2√2000) + (2(2000)/91125)

C'(2000) = (54/2(44.72)) + (4000/91125)

C'(2000) = 0.606 + 0.043

C'(2000) = 0.649

The marginal cost at the production level 2000 is $0.649.