Problems 627
10.2 Define the following terms:
(a)Cutting plane
(b)Gomory’s constraint
(c)Mixed-integer programming problem
(d)Additive algorithm
10.3 Give two engineering examples of a discrete programming problem.
10.4 Name two engineering systems for which zero–one programming is applicable.
10.5 What are the disadvantages of truncating the fractional part of a continuous solution for
an integer problem?
10.6 How can you solve an integer nonlinear programming problem?
10.7 What is a branch-and-bound method?
10.8 Match the following methods:
(a)Land and Doig Cutting plane method
(b)Gomory Zero–one programming method
(c)Balas Generalized penalty function method
(d)Gisvold and Moe Branch-and-bound method
(e)Reiter and Rice Generalized quadratic programming method
Problems
Find the solution for Problems 10.1–10.5 using a graphical procedure.
10.1 Minimizef= 4 x 1 + 5 x 2
subject to
3 x 1 +x 2 ≥ 2
x 1 + 4 x 2 ≥ 5
3 x 1 + 2 x 2 ≥ 7
x 1 , x 2 ≥ 0 ,integers
10.2 Maximizef= 4 x 1 + 8 x 2
subject to
4 x 1 + 5 x 2 ≤ 40
x 1 + 2 x 2 ≤ 12
x 1 , x 2 ≥ 0 ,integers
