II$.$ Formulating Linear Programming $[25$ points$]$

A contractor requires gravel at three construction sites and there are two nearby pits selling gravel. $180$

tons are available $($i$.$e$.$ for sale$)$ at the pit on the north side of town and $140$ tons are available at the pit on

the south side of town. The contractor needs the following amounts at the three construction sites:

The purchase price per ton of gravel at each pit and the transport cost per ton from each pit to each site

are given in the following table:

The contractor needs to determine how much gravel to transport from each pit to each site in order to

minimize the combined purchasing and transport costs.

Please state in English words only $($no math notation$),$ the:

Problem Objective:

Problem Constraint$($s$)$:

$2.$ Please define, using mathematical notation AND a description, the:

Decision Variable$($s$)$:

Input Parameter$($s$)$:

$3.$ Formulate the mathematical program associated with this optimization problem