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Unformatted text preview: University of Toronto Department of Mechanical and Industrial Engineering MIE468: Facility Planning (Winter 2012) Page 1 of 6 Midterm solutions Problem 1: (13 points) a) 55,000 barrels of gasoline = 2,310,000 gallons of gasoline 25,000 barrels of diesel = 1,050,000 gallons of diesel To produce 55,000 barrels of gasoline, need = , , . = , . , barrels of crude To produce 25,000 barrels of diesel, need = , , = , barrels of crude Since one barrel of crude produces both 19.6 gallons of gas and 10 gallons of diesel, then the total input is simply the max of the two amounts above: = { , } = , b) Let x = amount of extra gasoline output = amount of diesel output reduction Adjusting the previous equations: = , , . + , = , , To minimize the number of crude barrels needed, we want the above two quantities to be equal. Then we have to check to make sure x is between 0 and 1. Setting = , and solving for x, we get x = 0.75, which is between 0 and 1. Plugging this value into the equations for and , we get = { , } = { , , , } = , Problem 2: (12 points) a) machine 1 2 3 4 5 part 1 1 1 2 1 1 3 1 1 4 1 5 1 1 6 1 1 University of Toronto Department of Mechanical and Industrial Engineering MIE468: Facility Planning (Winter 2012) Page 2 of 6 b) i) DCA...
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 Spring '12
 PROF
 Industrial Engineering

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