hw05solutions

# hw05solutions - IEOR 162 Linear Programming Spring 2007...

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IEOR 162 Linear Programming Spring 2007 Homework 5 Solutions 3.review.50 (5 points) Data: c ij = distance between city i and incinerator j d jk = distance between incinerator j and landﬁll k p j = cost per ton for incinerator j w i = waste per day (in tons) for city i Variables: x ij = amount of waste to send from city i to incinerator j y jk = amount of debris to send from incinerator j to landﬁll k Formulation: min 2 i =1 2 j =1 ( p j + 3 c ij ) x ij + 2 j =1 2 k =1 3 d jk y jk s.t. 2 j =1 x ij = w i i = 1 , 2 (1) 2 j =1 y jk 200 k = 1 , 2 (2) 2 i =1 x ij = . 2 2 k =1 y jk j = 1 , 2 (3) x ij , y jk 0 i, j, k = 1 , 2 (4) 3.review.57 (5 points) Data: p i = price of fuel at location i d i = distance of leg i Variables: x i = amount of fuel to buy at location i y i = amount of fuel used on leg i I i = amount of fuel in plane’s tank at end of leg i Formulation: min 4 i =1 p i x i s.t. I 0 = 0 (1) I i 600 i = 1 , . . . , 4 (2) I i - 1 + x i 12000

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hw05solutions - IEOR 162 Linear Programming Spring 2007...

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