Answer:
Step-by-step explanation:
Given that:
If C(x) = the cost of producing x units of a commodity
Then;
then the average cost per unit is c(x) =
We are to consider a given function:
And the objectives are to determine the following:
a) the total cost at a production level of 1000 units.
So;
If C(1000) = the cost of producing 1000 units of a commodity
(b) Find the average cost at a production level of 1000 units.
Recall that :
the average cost per unit is c(x) =
SO;
Using the law of indices
c(1000) =$ 310.49 per unit
(c) Find the marginal cost at a production level of 1000 units.
The marginal cost is C'(x)
Differentiating C(x) = 54,000 + 130x + 4x^{3/2} to get C'(x) ; we Have:
(d) Find the production level that will minimize the average cost.
the average cost per unit is c(x) =
the production level that will minimize the average cost is c'(x)
differentiating to get c'(x); we have
Also
x= 0; or = = 30² = 900
Since production cost can never be zero; then the production cost = 900 units
(e) What is the minimum average cost?
the minimum average cost of c(900) is
c(900) = 60 + 130 + 4(30)
c(900) = 60 +130 + 120
c(900) = $310 per unit