# Inequality Constraints

• Jan 15th 2009, 12:56 AM
newatthis
Inequality Constraints
Hi I am trying to find out the constraints for the following:

A manufacturer makes cars and trucks

The cars have 4 wheels and take 30 mins to make
Trucks have 6 wheels and take 1 hour to make

The factory operates for 11 hours a day and the machine that makes the wheels can produce at most 80 wheels per day.

c = number of cars produced and t = number of trucks produced

What are some constraints on the manufacture of the trucks and cars

The constraints I have so far are:

1. c >= 0
2. t >= 0
3. c4 +t6 <=80

I'm unsure about the 3rd constraint, can someone help me out and let me know the 4th constraint and if the 3rd constraint is correct?

I feel like I have confused myself!
• Jan 15th 2009, 03:11 AM
Constraints
Hello newatthis
Quote:

Originally Posted by newatthis
Hi I am trying to find out the constraints for the following:

A manufacturer makes cars and trucks

The cars have 4 wheels and take 30 mins to make
Trucks have 6 wheels and take 1 hour to make

The factory operates for 11 hours a day and the machine that makes the wheels can produce at most 80 wheels per day.

c = number of cars produced and t = number of trucks produced

What are some constraints on the manufacture of the trucks and cars

The constraints I have so far are:

1. c >= 0
2. t >= 0
3. c4 +t6 <=80

I'm unsure about the 3rd constraint, can someone help me out and let me know the 4th constraint and if the 3rd constraint is correct?

I feel like I have confused myself!

Your 3rd constraint is OK, but you would usually write $4c+6t \le 80$, which then simplifies to $2c + 3t \le 40$.

To get the other constraint(s), just look at the time each vehicle takes to make. If we assume (although it doesn't actually say so in the question) that at any given moment, the factory is either making a car or a truck (and can't therefore make them both at the same time) then the total time taken to make $c$ cars and $t$ trucks is $0.5c + t$ hours. And this is less than or equal to ... what?

On the other hand, if the factory can make both vehicles at the same time, then there will be two further constraints: one on the number of cars that can be made in a day, and a separate one on the number of trucks.