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Winston: Telfa Corporation tables and chairs (pure integer program)

ToolLinear Programming
SourceWinston, W. L. (2004). Operations Research: Applications and Algorithms, 4th ed. Thomson Brooks/Cole, Belmont, CA. Section 9.3.
LevelUndergraduate

Problem

Telfa makes tables (x1, profit 8) and chairs (x2, profit 5) with x1 + x2 ≤ 6 and 9 x1 + 5 x2 ≤ 45; both must be whole numbers. Find the integer production plan that maximizes profit and compare it with the LP relaxation.

Inputs to Enter

  • max 8 x1 + 5 x2
  • x1 + x2 <= 6 ; 9 x1 + 5 x2 <= 45
  • int x1, x2
Open the Linear Programming tool

Answers

  • LP relaxation: Z = 165/4 = 41.25 at x1 = 3.75, x2 = 2.25
  • Integer optimum: Z = 40 at x1 = 5, x2 = 0
  • The two-variable drawing shows the lattice points inside the feasible region

Notes

Type the model in place of the default problem. Not the default case.

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