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. The marginal cost is the rate of change of the cost with respect to the number of items produced, that is, the derivative C'(x). (a) 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 produc- tion level of 1000 units; (ii) the production level that will minimize the average cost; and (iii) the minimum average cost.

ENGR.ECONOMIC ANALYSIS
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Chapter1: Making Economics Decisions
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interest). At what age is the rate of disease development the
highest?
Source: Adapted from P. Coleman et al., “Endemic Stability―A Veterinary
Idea Applied to Public Health," The Lancet 357 (2001): 1284–86.
19. 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. The marginal
cost is the rate of change of the cost with respect to the
number of items produced, that is, the derivative C'(x).
(a) 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 produc-
tion level of 1000 units; (ii) the production level that
will minimize the average cost; and (iii) the minimum
average cost.
20. If R(x) is the revenue that a company receives when it sells
x units of a product, then the marginal revenue function is
the derivative R'(x). The profit function is
Transcribed Image Text:interest). At what age is the rate of disease development the highest? Source: Adapted from P. Coleman et al., “Endemic Stability―A Veterinary Idea Applied to Public Health," The Lancet 357 (2001): 1284–86. 19. 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. The marginal cost is the rate of change of the cost with respect to the number of items produced, that is, the derivative C'(x). (a) 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 produc- tion level of 1000 units; (ii) the production level that will minimize the average cost; and (iii) the minimum average cost. 20. If R(x) is the revenue that a company receives when it sells x units of a product, then the marginal revenue function is the derivative R'(x). The profit function is
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