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Unformatted text preview: (d) Is it necessary to increase the inspection and packaging time to reach the maximum proﬁt? 3. Consider the problem max x 1 + 2 x 2 + 3 x 3 s.t. x 1 + 2 x 2 + 3 x 3 ≤ 10 x 1 + x 2 ≤ 5 x 1 ≤ 1 x 1 ,x 2 ,x 3 ≥ Find all optimal basic feasible solutions and write a general expression for all (basic and nonbasic) optimal solutions. 1 4. Consider the following problem: max 3 x 1 + x 2 s.t. x 1 + 2 x 2 ≤ 5 x 1 + x 2x 3 ≤ 2 7 x 1 + 3 x 25 x 3 ≤ 20 x 1 ,x 2 ,x 3 ≥ (a) In which direction is the solution space unbounded? (b) Without further computations, can one conclude that the problem has no bounded optimal solution? If not, ﬁnd the optimal solution. (c) Is the optimal solution degenerate? 5. Solve the following minimization problem: min 4 x 1 + 4 x 2 + x 3 s.t. x 1 + x 2 + x 3 ≤ 2 2 x 1 + x 23 x 3 ≥ 5 x 1 ,x 2 ,x 3 ≥ . 2...
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 Spring '10
 TanBanPin
 Math, Optimization, Dyeing Sewing Inspection & Packaging

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