MAS 801 It's a Discreetly Discrete World – Mathematics in Real-life ...

Lecture 9: 22 October 2008
Proving Optimality: Method of Tight Restrictions
• The method of tight restrictions tries to combine the constraints to
show that the objective function value must be greater than some value
p or less than some value q
• Let’s illustrate this with an example
maximize
z = 1000x + 3000y
subject to x + 2y ≤ 300
x + 5y ≤ 600
x ≥ 0
y ≥ 0
• First note that the point (100,100) gives an objective function value of
400000
• If we can combine the constraints to show that 1000x + 3000y ≤ 400000,
then (100,100) must be optimal