ieor162-sp11-mt1-Chen-exam

# ieor162-sp11-mt1-Chen-exam - Department of Industrial...

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IEOR162 Linear Programming Midterm Exam 1 Spring 2011 Name: Grade: 1. (30 points) Consider the following linear program z * = min x 1 + x 2 s.t. x 1 - 2 x 2 4 (1) 2 x 1 + x 2 ≥ - 2 (2) 3 x 1 - 4 x 2 12 . (3) (a) (10 points) Draw the constraints and then shade the feasible region. (b) (5 points) Draw an isoproﬁt line. Indicate the improving direction on the graph. x x 1 2 (c) (5 points) Write down the binding constraints at the point (4 , 0). (d) (5 points) Find an optimal solution or claim that the LP is infeasible or unbounded. (e) (5 points) Repeat Part (d) with the new objective function “max x 1 - x 2 ”. 1

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2. (25 points) A factory uses two materials and one machine to produce two products. The amount of product 1 produced is the sum of materials 1 and 2 input. For example, if we input 5 pounds of material 1 and 10 pounds of material 2 into the machine, we will produce 15 pounds of product 1. To meet the quality requirement for product 1, the proportion of material 2 must be at least 30%. Producing one pound of product 1 requires 2 hours of the
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## This note was uploaded on 09/01/2011 for the course IEOR 162 taught by Professor Zhang during the Spring '07 term at Berkeley.

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ieor162-sp11-mt1-Chen-exam - Department of Industrial...

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