During the 1950s the wholesale price for chicken for a country fell from 25¢ per pound to 14¢ per pound, while per capita chicken consumption rose from 23.5 pounds per year to 29 pounds per year. Assume that the demand for chicken depended linearly on the price. (a) Construct a linear demand function q(p), where p is in cents (e.g., use 14¢, not $0.14). Then, find the revenue function. R(p). R(p) (b) What wholesale price for chicken would have maximized revenues for poultry farmers? ¢ per pound Second derivative test: Your answer above is a critical point for the revenue function. To show it is a maximum, calculate the second derivative of the revenue function. R"(p)=
During the 1950s the wholesale price for chicken for a country fell from 25¢ per pound to 14¢ per pound, while per capita chicken consumption rose from 23.5 pounds per year to 29 pounds per year. Assume that the demand for chicken depended linearly on the price. (a) Construct a linear demand function q(p), where p is in cents (e.g., use 14¢, not $0.14). Then, find the revenue function. R(p). R(p) (b) What wholesale price for chicken would have maximized revenues for poultry farmers? ¢ per pound Second derivative test: Your answer above is a critical point for the revenue function. To show it is a maximum, calculate the second derivative of the revenue function. R"(p)=
Algebra and Trigonometry (MindTap Course List)
4th Edition
ISBN:9781305071742
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter2: Functions
Section2.4: Average Rate Of Change Of A Function
Problem 4.2E: bThe average rate of change of the linear function f(x)=3x+5 between any two points is ________.
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