Solution Found!
?(a) If ????(????) is the cost of producing ???? units of a commodity, then the average
Chapter 4, Problem 65(choose chapter or problem)
(a) 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. Show that if the average cost is a minimum, then the marginal cost equals the average cost.
(b) If 𝐶(𝑥) ＝ 16,000 + 200x + 4𝑥3/2, in dollars, find (i) the cost, average cost, and marginal cost at a production level of 1000 units; (ii) the production level that will minimize the average cost; and (iii) the minimum average cost.
Questions & Answers
QUESTION:
(a) 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. Show that if the average cost is a minimum, then the marginal cost equals the average cost.
(b) If 𝐶(𝑥) ＝ 16,000 + 200x + 4𝑥3/2, in dollars, find (i) the cost, average cost, and marginal cost at a production level of 1000 units; (ii) the production level that will minimize the average cost; and (iii) the minimum average cost.
ANSWER:
Step 1 of 2
a)
We have
Using the quotient rule
