Week #12
"God made the integers, and all the rest is the work of man." -- Leopold Kronecker (1823-1891)
I once thought that too, but I was then exposed to optimization problems where the solution set was restricted to the integers. As you know our solutions are not restricted to the integers, but are instead allowed to be any physically reasonably real number. However, in real optimization problems it is often unrealistic to talk about solutions that are not integers. For example, when FedEx is buying planes to ship items they cannot purchase 1.3 planes. So, some may reason that they should just round off. Not so. Try this simple problem (pre-calc, no calculus involved):
The solution when x is not restricted to the integers is (376/193, 950/193), but if we have to restrict x to integer values only, the solution is (5, 0) which is a long way off from (376/193, 950/193).
What's the point? Don't think you can willy nilly round to get answers that are integers!
I once thought that too, but I was then exposed to optimization problems where the solution set was restricted to the integers. As you know our solutions are not restricted to the integers, but are instead allowed to be any physically reasonably real number. However, in real optimization problems it is often unrealistic to talk about solutions that are not integers. For example, when FedEx is buying planes to ship items they cannot purchase 1.3 planes. So, some may reason that they should just round off. Not so. Try this simple problem (pre-calc, no calculus involved):
Maximize:
x1 + 0.64x2
Subject to the following constraints:
50x1 + 31x2 <= 250
3x1 - 2x2 >= -4
x1, x2 >=0
The solution when x is not restricted to the integers is (376/193, 950/193), but if we have to restrict x to integer values only, the solution is (5, 0) which is a long way off from (376/193, 950/193).
What's the point? Don't think you can willy nilly round to get answers that are integers!
posted by Ron Bannon at
11/19/2004 07:56:00 AM
1 Comments:
I've been accused of being the world's biggest cynic, and I am severely depressed about the results from the last quiz. The scores were: 9.5, 9, 8, 8, 7.67, 7, 7, 6.5, 6, 5, 5, 4, 4, 4, 3.83, 3, 3, 1.5, 1.5, 1.5, 1, 1. Well, maybe it was too tough and I will certainly go over the gory details of how to do the problem on Monday. In any case, you should download the answer key.
Also, if I made an error you can get credit by pointing it out. First come first serve for credit though.
By
Ron Bannon, at 2:47 PM
Post a Comment
<< Home