F1 F2 2) Oilco has oil fields in San Diego and Los Angeles. The San Diego field
ID: 371328 • Letter: F
Question
F1 F2 2) Oilco has oil fields in San Diego and Los Angeles. The San Diego field can produce up to 500,000 barrels per day, and the Los Angeles field can produce up to 400,000 barrels per day. Oil is send from the fields toa refinery either in Dallas or in Houston (assume each refinery has unlimited capacity). It costs $700 to refine 100,000 barrels of oil in Dallas and $900 to refine 100,000 barrels of oil in Houston. Refined oil is shipped to customers in Chicago and New York. Chicago customers require 400,000 barrels per day of refined oil and New York customers require 300,000 barrels per day. The cost of shipping 100,000 barrels of oil (refined or unrefined) between cities are given in the table. Formulate and solve a transhipment model of the situation. 0 Dallas Houston New York Chicago From Los Angeles $300 $110 San Diego Dallas Houston $420 $100 $450 $550 $470 $530Explanation / Answer
Refinery Cost
D=700*x1/100000
H=900*x2/100000
Capacity Constraint
SA <= 500000
LA<= 400000
Demand Constraint
NA>= 300000
C>=400000
As both the customer require the Refined oil therefore refineries have to refine the crude oil first and then send therefore suppose x1 and x2 be amount of oil Dallas and Houston get from the San Diego and Los Angles respectively
X1= LAD+SAD
X2=LAH+SAH
Objective it to minimise the total cost including the transportation
Minimise = 1/100000{700*(LAD+SAD) + 900*(LAH+SAH) + 300*LAD+110*LAH+420*SAD+110*SAH+450*DN+550*DC+470*HN+530*HC}
Subject to:
LAD+LAH<=500000
SAD+SAH<=400000
DN+HN>=300000
DC+HC>=400000
LAD+SAD>=DN+DC
LAH+SAH>=HN+HC
LAD, LAH, SAD, SAH, DN, HN, DC, HC >=0, Integer Values
Dallas Houston Los Angles LAD LAH <= 500000 San Diego SAD SAH <= 400000 New York Chicago Dallas DN DC Houston HN HC >= >= 300000 400000Related Questions
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