I've got a funny result and I believe that it is wrong, but I send it to you nevertheless:
The revenue is calculated by weight * price per pound. The result is the money the farmer gets from every chicken eating American.
The weight went up by 5.5 pounds when the price goes down by 11 cts. Thus: Decreasing the price by 1 ct. would increase the weight by 0.5 pounds.
Let x be the number of cents the price per pound decreases.
r is the revenue
w is the weight
p is the price per pound:
r = w * p
If the price changes you get:
r(x) = (22+0.5x)(25-x) = -0.5x² - 9.5x + 550
The graph of this function is a parabola opening downward. The vertex of the parabola is the maximum of the function. The x-coordinate of the vertex is (-b)/(2a). The maximum will be reached if x = (-(-9.5))/(2*(-0.5)) = -9.5
You have to increase the price to 34.5 cts per pound. The consumption will go down to 17.5 pounds per person and then the revenue will be 595.125 cts per chicken eating person.
Well this result is confusing me a lot, but I cann't detect my mistake. Maybe you are more successfull. Good luck!