Linear Programming Constraints

[Jarryd12]

Hey guys, Just wondering if someone could give me a hand with this. I'm unable to work out the constraints in the problem. Anyone have an idea how to proceed? Cheers

The transport authority in a major city has promoted the use of buses and trains to those who will attend sporting events at a new stadium complex built for a world championship. While this is desirable to avoid traffic problems, it also offers the transport authority an opportunity to gain revenue from public transport. A maximum of 170,000 people are expected to arrive at the stadium complex in any one day, but at least 36,000 will use private transport. The number of buses that can arrive in one hour is 60, each with a capacity of 70 people. The number of trains that can arrive per hour is 20, each carrying up to 500 people.
Buses and trains arrive at the stadium complex for 10 hours per day. The number of people travelling by bus is at least 25%% of the number coming by train. Bus tickets cost $6 and train tickets cost $4 per person. The transport authority wants to maximise revenue.


(i) Set up the object function and all constraints for this problem clearly identifying the variables used.




so.. x= number of trains , y= number buses

36000<70y+500x<170000 (<or=)
y<600
x<200
y>0.25x

Dont think these are right to be honest..

 

[stapel]

so.. x= number of trains , y= number buses

36000<70y+500x<170000 (<or=)
y<600
x<200
y>0.25x

Dont think these are right to be honest..

It might help if you provided your reasoning. For instance, where are the "600" and "200" coming from? Thank you!

 

[JeffM]

Hey guys, Just wondering if someone could give me a hand with this. I'm unable to work out the constraints in the problem. Anyone have an idea how to proceed? Cheers

The transport authority in a major city has promoted the use of buses and trains to those who will attend sporting events at a new stadium complex built for a world championship. While this is desirable to avoid traffic problems, it also offers the transport authority an opportunity to gain revenue from public transport. A maximum of 170,000 people are expected to arrive at the stadium complex in any one day, but at least 36,000 will use private transport. The number of buses that can arrive in one hour is 60, each with a capacity of 70 people. The number of trains that can arrive per hour is 20, each carrying up to 500 people.
Buses and trains arrive at the stadium complex for 10 hours per day. The number of people travelling by bus is at least 25%% of the number coming by train. Bus tickets cost $6 and train tickets cost $4 per person. The transport authority wants to maximise revenue.


(i) Set up the object function and all constraints for this problem clearly identifying the variables used.




so.. x= number of trains , y= number buses OK You identified and NAMED the relevant variables, but you left out a key element of the definition. Are these variables per hour or per day? If Dr. Phil were here, he would tell you how critical it is to identify your units.

36000<70y+500x<170000 (<or=) As you imply, these need to use \(\displaystyle \le.\)

y<600 There is an important conceptual error here. Constraint should include non-negativity: \(\displaystyle 0 \le y \le 600.\)

x<200 There is an important conceptual error here. Constraint should include non-negativity: \(\displaystyle 0 \le x \le 200.\)

y>0.25x \(\displaystyle y \ge 0.25x.\)

Dont think these are right to be honest. They were a quite decent effort

.

Now what about the objective function? Give it a go.