Question

During the 1950s the wholesale price for chicken for a country fell from 25 cents per pound to 14 cents 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 (in cents per pound) for chicken would have maximized revenues for poultry farmers? What would have that revenue amounted to per year?

Answer 1

Consider the following explanation.

Step-by-step explanation:

First off, lets make an equation for it. You have your x and y. With x being the price and y being your output, the pounds.

So you split it up to (.25,21.5) and (.14,27). Then do the y2-y1/x2-x1 for slope, gets you -50. Put that into y=mx+b and solve for b. B is found with being 34. Then put it all together for your demand equation. q=-50p+34 is your demand. Then get revenue which is pq so -50p^2+34p. Do the derivative of your revenue and set = to 0 for maximum revenue price. So -100p=-34. Divide and you get .34 which is your max price for max revenue. For revenue, just plug your price back into your original revenue equation.