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?

A linear relationship must have a general equation of y = mx + b. The independent variable is the price which is x, and the dependent variable is the demand which is y. Since we have two points, we find the slope.

m = (27 - 21.6) / (14 - 25) = -0.5
Thus, y = -0.5x + b
27 = -0.5(14) + b
b = 34

Equation would be y = -0.5x + 34; Revenue is price times demand or  xy. Thus, R = ( -0.5x + 34)x. Simplifying, R = -0.5x^2 + 34x

To find the maximum revenue, we differentiate and equate to zero. 

dR/dx = 0 = -x + 34
x = 34

Thus, the wholesale price for chicken should be $34 for maximum revenue.

Answer:

$4034.40

step-by-step explanation:

the perimeter of the field is the sum of the lengths of the four sides:

47 yd + 158 yd + 47 yd + 158 yd = 410 yd

the cost of 3 ft (1 yd) of fence is 3×$3.28 = $9.84.

so the cost of jake's wood perimeter fance is

(410 yd) × ($9.84 /yd) = $4034.40