Final answer:
To answer the questions, we need to apply the given cost function C(x) = √54x + 27000x^2, find the cost at the production level 2000, the average cost at the production level 2000, the marginal cost at the production level 2000, the production level that will minimize the average cost, and the minimal average cost.
Step-by-step explanation:
To find the answers to the questions, we need to apply the given cost function C(x) = √54x + 27000x^2.
a) To find the cost at the production level 2000, we substitute x = 2000 into the cost function and calculate C(2000).
b) To find the average cost at the production level 2000, we divide the cost C(2000) by the production level 2000.
c) The marginal cost at the production level 2000 can be found by taking the derivative of the cost function C(x) with respect to x and then substituting x = 2000.
d) To find the production level that will minimize the average cost, we need to find the minimum point on the average cost curve. This can be done by finding the derivative of the average cost function and solving for x.
e) The minimal average cost can be found by substituting the production level obtained in part d) into the average cost function.