Question

For the given cost function C(x) = 54\sqrt{x}+\frac{x^2}{27000} find
a) The cost at the production level 1350
b) The average cost at the production level 1350
c) The marginal cost at the production level 1350
d) The production level that will minimize the average cost.
e) The minimal average cost.

Answer 1

for the first part you simply have to substitute the value 1350 for x
for second part you have to divide the cost found in part one by 2
for marginal cost differentiate the cost function f(x)wrt x and then put value 1350 for x

Answer 2

for the production level that will minimize the cost, equate the marginal cost to zero, then solve for x.

Answer 3

after that, test if its the minimum value for x, using first derivative test.