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Unformatted text preview: Department of Industrial Engineering & Operations Research IEOR162 Linear Programming Midterm Exam 1 Fall 2011 Name: Grade: 1. (20 points) A factory produces two kinds of products by assembling 2 kinds of components. One unit of product 1 requires one unit of component 1 and two units of component 2. One unit of product 2 requires two units of component 1 and three units of component 2. The unit purchasing costs of components 1 and 2 are $50 and $10, respectively. The unit selling prices of products 1 and 2 are $120 and $200, respectively. The factory only has $1000 to purchase components. At most ten units of component 1 can be purchased. Formulate an LP that can maximize the factorys sales revenue. 1 2. (25 points) Consider the following LP z * = min 3 x 1 2 x 2 + x 3 s.t. 2 x 1 3 x 2  6 (1) x 1 + x 2  2 (2) x 1 + x 2 x 3 (3) x 1 . (4) (a) (5 points) Find an equivalent LP with only variables x 1 and x 2 and three constraints. (b) (10 points) For the twovariable LP in Part (a), draw the constraints, shade the feasible region, draw an isoprofit line, and indicate the improving direction....
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 Fall '07
 Zhang
 Operations Research

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