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 21.5 pounds per year to 27 pounds per year. Assuming that the demand for chicken depended linearly on the price, what wholesale price for chicken would have maximized revenues for poultry farmers? 34 Correct: Your answer is correct. ¢ per pound What would have that revenue amounted to? (Round your answer to the nearest cent.)

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sampsonola sampsonola · Answer 1 · 2020-02-27T11:59:49+01:00

Answer:

$ 5.78

Step-by-step explanation:

linear function is define by the equation y = mx + c

where x = price and y = consumption

when x = 25¢, y = 21.5 pounds

x = 14¢, y = 27 pounds

replacing x and y in the equation

21.5 pounds = 25¢ m + c

27 pounds = 14¢ m + c

subtract equation 2 from equation 1

- 5.5 pounds = 11¢ m

m = - 5.5 pounds / 11¢ = -0.5 pounds / ¢

substitute m into any of equation 1 and 2

21.5 pounds = 25¢ (-0.5 pounds / ¢ ) + c

21.5 = - 12.5 + c

c = 21.5 + 12.5 = 34

y = -0.5 x + 34

revenue = p × q = x × y = x (-0.5 x + 34) = -0.5x² + 34x

differentiate the function and set dy/dx to zero to find wholesales price that maximizes revenue

dy/dx = -x + 34 = 0

-x = -34

x = 34¢

revenue = -0.5x² + 34x = -0.5 (34)² + (34 × 34) = 578¢ = $ 5.78