Question

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

Answer 1

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

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there is a agreement ot use atleast 10 trains

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There are not more than 66 buses available

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The total cost should be no more than $2,700,000

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Finally the linear model is

Minimize

s.t.

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• 

• 

• 
• 

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