hw1sol - Operations Research, GE330 - IE 310 Homework 1...

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Unformatted text preview: Operations Research, GE330 - IE 310 Homework 1 Solutions Exercise 1 : (a) maximize x 1 x 2 subject to x 1 + x 2 = 2 It is not a linear program, since the objective function is not a linear function. (b) maximize x 1 subject to x 1 + x 2 = 2 x 2 1- x 2 2 It is not a linear program, since the second constraint is not linear. (c) minimize x 1 + x 2 subject to x 1- x 2 1 x 1 + x 2- x 3 5 It is a linear program, since the objective function and all the constraints are linear. (d) maximize x 1 + x 2 subject to x 1- x 2 1 x 1 and x 2 are integers It is not a linear program, since the variables are constrained to integer values. (e) minimize x 1- x 2 + x 4 subject to x 1- x 2 3 x 4 4 x 1 , x 2 It is a linear program, since the objective function and all the constraints are linear. 1 Exercise 1, page 15 : We know that: x 1 = Tons produced daily of exterior paint x 2 = Tons produced daily of exterior paint So in order for each constraint to hold: (a) x 2- x 1 1, or equivalently...
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hw1sol - Operations Research, GE330 - IE 310 Homework 1...

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