n 1997 Fuller and coworkers at Texas A&M University estimated the operating costs of cotton gin plants of various sizes. The operating costs of the next to the smallest plant is shown in the following table. x 2000 4000 6000 8000 10000 12000 y 163,200 230,480 301,500 376,160 454,400 536,400 Here x is the annual number of bales produced, and y is the dollar total cost. (Use 4 decimal places in your answer.) A. Determine the best fitting line using least squares. Also determine the square of the correlation coefficient. The best fitting line is C(x) =

In 1997 Fuller and coworkers at Texas A&M University estimated the operating costs of cotton gin plants of various sizes. The operating costs of the next to the smallest plant is shown in the following table.

Here x is the annual number of bales produced, and y is the dollar total cost. (Use 4 decimal places in your answer.)
A. Determine the best fitting line using least squares. Also determine the square of the correlation coefficient.
The best fitting line is C(x) = 

 .
The square of the correlation coefficient is r² = 

 .

B. The study noted that revenue was $63.25 per bale. At what level of production will this plant break even?
The revenue equation is R(x) = 

The profit equation is P(x) = 

The production will break even when 

 bales are produced.

C. What are the profits or losses when production is 3000 bales? 4000 bales? (Round to the nearest cent.)
When 3000 bales are produced, the gin experiences a  (loss, profit) of $  . When 4000 bales are produced, the gin experiences a  (loss, profit) of $