Write the complete algebraic formulation of a linear model for the following business decision scenario:

The city of Tall Pines is constructing a major road project and has contracted with Big Bob's Evacuation to do the earthwork movement for the project. The project involves moving several thousand cubic yards of earth to be removed from portions of the existing street $($known as "cut" portions$)$ and to be deposited in other portions $($known as "fill" portions$).$

Big Bob has discovered an error in the bidding estimate he made. He now realizes the only way his company is going to make any profit from the project is to minimize the amount of travel of the earthmoving equipment in completing the project $($which is equivalent to assuming the cost to move one cubic yard of earth one foot is the same for every possible move in the project$).$

The $4000-$foot street being reworked runs exactly north and south and has been subdivided into $500-$foot long designated cut and fill portions by the Tall Pines Engineering Department, with the following facts pertaining to these portions:

Portion

$($feet from south end of street$)$

If Cut Portion, Available yd$^3$ earth

#$1$:$0-500$

$7,000$

#$2$: $500-1,000$

$3,000$

#$3$: $1,000-1,500$

$10,000$

#$4$: $1,500-2,000$

$12,000$

#$5$: $2,000-2,500$

$9,000$

#$6$: $2,500-3,000$

$6,000$

#$7$: $3,000-3,500$

$4,000$

#$8$: $3,500-4,000$

$5,000$

If additional earth is needed, Tall Pines has contracted with a Mr$.$ Jones $-$ whose property is $500$ feet directly west of the middle of Portion #$6($and for which access to the street project will have to be by traveling on a line exactly west$/$east from$/$to the street$)-$ to allow Big Bob's Evacuation to obtain needed earth. Unfortunately, the earth available from Mr$.$ Jones' property is not considered appropriate for use in Portion #$5$ of the street project.

It is reasonable to treat the location of earth to be moved from cut portions, and the location of deposits of earth in fill portions, as being at the center of the respective portions.

If Fill Portion, Available yd$^3$ earth