If C ( x ) is the cost of producing x units of a commodity, then the average cos
ID: 2840721 • Letter: I
Question
If C(x) is the cost of producing x units of a commodity, then the average cost per unit is c(x) = C(x)/x. Consider the cost function C(x) given below. (Round your answers to the nearest cent.)
C(x) = 54,000 + 240x + 4x3/2
(a) Find the total cost at a production level of 1000 units.
(b) Find the average cost at a production level of 1000 units.
(c) Find the marginal cost at a production level of 1000 units.
(d) Find the production level that will minimize the average cost.
(e) What is the minimum average cost?
Explanation / Answer
a. x = 1000 so plug x into equation to get $231,600.
b. 231,600/1000 = $231.6 / unit.
c. Marginal Cost dTC/dQ = 150 + 3/2 (6x^0.5) or the derivative of Total Cost with respect to Quantity. So for x = 1000 Marginal Cost = 150 + 9(1000^0.5) = $434.60 for an additional unit produced.