Jonathan Macintosh is a highly successful Pennsylvania orchardman who has formed a company to produce and package applesauce. Apples can be stored for several months in cold storage, so applesauce production is relatively uniform throughout the year. The recently hired controller for the firm is about to apply the high$-$low method in estimating the company$$s energy cost behavior. The following costs were incurred during the past $12$ months:

Month

Pints of Applesauce Produced

Energy Cost

January

$36,500$

$ $24,900$

February

$22,500$

$23,600$

March

$23,500$

$23,500$

April

$25,500$

$23,950$

May

$31,500$

$24,400$

June

$33,500$

$24,850$

July

$41,500$

$29,500$

August

$31,500$

$24,300$

September

$31,500$

$24,500$

October

$29,500$

$24,200$

November

$42,500$

$25,600$

December

$40,500$

$26,450$

Required:

Use the high$-$low method to estimate the company$$s energy cost behavior and express it in equation form. Use the formula Y $=$ a $+$ bX$,$ where Y denotes energy cost for a month and X denotes pints of applesauce produced.

Predict the energy cost for a month in which $41,000$ pints of applesauce are produced.