I came across a LP problem in which a factory recruited workers on daily basis giving them wages per day. I don't remember the figures but I remember what was in the question. We had to find the number of male and female workers which should be recruited so as to minimise the the total expenditure on their wages. On solving through graphical method (the only method I know) the answer came out to be in fractions. How can the number of female or male workers be fractional? Out of three corner points 2 were fractional so I wrote the 3rd point saying that workers cannot be fractional. What would be the correct answer?
Asked
Active
Viewed 764 times
0
-
2You might of course have part-time workers ... – Hagen von Eitzen Jan 31 '16 at 15:08
-
And workaholics. – mvw Jan 31 '16 at 15:10
-
A practical answer is to round up the numbers of workers to the next whole number. This may not be optimal. If your solution is $2.5$ men, $4.7$ women, you know you can get done with $3$ men, $5$ women, but having the extra women may mean you don't need the last man. The next ones to check would be $2,5$ and $3,4$ to see if you get done. – Ross Millikan Jan 31 '16 at 15:18
2 Answers
0
If the variables are restrained to integer values, as they seem in this case, you have an integer linear programming problem, with its own solutions methods.
Many LP solvers, like lp_solve, offer to model ILP problems as well.
mvw
- 34,562
0
It doesn't follow that the third corner point is the best integral solution. Graphically, what you want is the best grid point (both variables a whole number), so having determined the slope of the objective function, slide its line left-downwards (as you're minimising) as far as possible while still passing through one.
GarryB
- 94