Chapter 7, Problem 14RP

Explanation of Solution

Assumptions:

• Let LAD and LAH represent the number of “100000” barrels of oil shipped from Los Angeles (L.A.) to Dallas and Houston, respectively.
• Let SDD and SDH represent the number of “100000” barrels of oil shipped from San Diego to Dallas and Houston, respectively.
• Let DNY and DC represent the number of “100000” barrels of oil shipped from Dallas to New York (N.Y.) and Chicago, respectively.
• Let HNY and HC represent the number of “100000” barrels of oil shipped from Houston to N.Y. and Chicago, respectively.

Formulation:

• It is given that in L.A., a maximum of “400000” barrels of oil are able to be produced per day. It is represented by,

  LAD+LAH<=4

• It is given that in San Diego, a maximum of “500000” barrels of oil are able to be produced per day. It is represented by,

  SDD+SDH<=5

• From the table, the cost of shipping “100000” barrels of oil between the cities L.A. and Dallas is “300”, and the cities San Diego and Dallas is “420”.
• Hence, the total cost of shipping the barrels of oil from L.A. and San Diego to Dallas is as follows,

  ${\text{Cost}}_{\text{D}}\text{=300LAD+420SDD}$

• From the table, the cost of shipping “100000” barrels of oil between the cities L.A. and Houston is “110”, and the cities San Diego and Houston is “100”.
• Hence, the total cost of shipping the barrels of oil from L.A. and San Diego to Houston is as follows,

  ${\text{Cost}}_{\text{H}}\text{=110LAH+100SDH}$

• It is given that in Dallas, the cost of refining oil per “100000” barrels, is “$700”. It is represented by,

  ${\text{Cost}}_{\text{refD}}\text{=700}\left(\text{LAD+SDD}\right)$

• It is given that, the cost of refining oil per “100000” barrels, is “$900” in Houston. It is represented by,

  ${\text{Cost}}_{\text{refH}}\text{=900}\left(\text{LAH+SDH}\right)$

• Given that Chicago customer needs refined oil of at least “400000” barrels of oil per day. It is represented by,

  DC+HC>=4

• Given that N.Y. customer needs refined oil of at least “300000” barrels of oil per day. It is represented by,

  DNY+HNY>=3

• From the table, the cost of shipping “100000” barrels of oil between the cities Dallas and N.Y.is “450”, and the cities Houston and N.Y. is “470”.
• Hence, the total cost of shipping the barrels of oil from Dallas and Houston to N.Y. is as follows,

  ${\text{Cost}}_{\text{NY}}\text{=450DNY+470HNY}$

• From the table, the cost of shipping “100000” barrels of oil between the cities Dallas and Chicago is “550”, and the cities Houston and Chicago is “530”