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 depends linearly on the price, what wholesale price for chicken maximizes revenues for poultry farmers?

Question

amistre64 · Answer

there should be some formulas in your material that relates to this that you can offer us.

amistre64 · Answer

25 is to 21.5
        as
14 is to 27

-11 is to +5.5  so the rate of change is 5.5/-11 = -.5

amistre64 · Answer

D(p) = -.5p + 9

seems to be the demand equation

anonymous · Answer

There was no formula given the questions ask:
a) cents per pound
b)What does that revenue amount to? per year

amistre64 · Answer

or is that the supply equation?

amistre64 · Answer

the question does not exist in a vacuum' it is based on the material in the current "chapter" of the material that you are studying i would assume; or at least based on material that you have covered in the past

anonymous · Answer

Think of the demand of chicken (i.e. consumption of chicken, pounds/yr) as a function of price of chicken (i.e. wholesale price, cents/pound). The information in the question clearly tells you that when Price=25, Demand=21.5. And when Price=14, Demand=27. Also, it says that demand depends linearly on the price. So you can plot those two points on a graph of Demand on the y-axis against Price on the x-axis, and then connect those two points linearly.The graph will have $$gradient=\Delta demand/\Delta price=-0.5$$You can then extrapolate the graph to find the y-intercept, which is 34. So the equation of the graph will be $$D(P)=-0.5P+34$$ This is our demand function.

For the next part, we want to find the price where revenue is maximized. We know that revenue is simply quantity sold times the price it was sold at. i.e. $$Rev=Quantity \times Price=D(P)\times P=(-0.5P+34)\times P=-0.5P ^{2} +34P$$Differentiate the function with respect to P and then equate it to zero. Then solve for P. That will be the price where revenue is maximized. That is the answer to part (a).
For part (b), simply plug in the price found in (a) into the equation for Revenue above, then you have your answer.

anonymous · Answer

i cant get part b for mine, we have the exact same problems, the numbers are the same, how did you do part b?

anonymous · Answer

Thank you @quest326 your answer was right! But I was wondering, in the demand equation which is : D(P) = -0.5P + 34; is there a way to find 34 without extrapolating the graph please?