In: Statistics and Probability
Suppose that you have been given the job of providing advance transport to a new exhibition hall and it is possible to use existing railway connections and bus routes. Each bus will cost $30000 and carry 40 passengers. Each railway train will cost $45000 and carry 50 passengers. A bus can make 15 trips a day and a railway train 12 trips a day. The system has a number of financial and design constraints. It must carry at least 48000 passengers a day and cost no more than $2700000. There is also an agreement to use at least 10 trains, while no more than 66 buses are available. What is the minimal cost solution to this problem? Linear programming explains all the steps please
Let T be the number of trains and B be the number of buses that are needed.
These are the decision variables
Each bus costs $30,000. Hence B buses would cost $30000B
Each train costs $45,000. Hence T trains would cost $45000T
The total cost of transport is
We want to minimize this cost. Hence this is the objective function
Finally the constraints
T trains can carry 50T passengers in each trip and 50T*12 =600T in a day and B bus can carry 40B passengers in each trip and 40B*15 = 600B in a day. The total passengers to be carried per day is at least 48000
there is a agreement ot use atleast 10 trains
There are not more than 66 buses available
The total cost should be no more than $2,700,000
Finally the linear model is
Minimize
s.t.
Prepare the following spreadsheet
with the following values
set the solver using data-->solver
and get the following solution
For a minimum cost solution, we need to use 66 buses and 14 trains