Question

Oranges are grown, picked, and then stored in warehouses in Tampa, Miami, and Fresno. These warehouses supply oranges to markets in New York, Philadelphia, Chicago, and Boston. The following table shows the shipping costs per truckload (in hundreds of dollars), supply, and demand. Because of an agreement between distributors, shipments are prohibited from Miami to Chicago:To (cost, in $100s)From New York Philadelphia Chicago Boston SupplyTampa $ 9 $ 14 $ 12 $ 17 200Miami 11 10 6 10 200Fresno 12 8 15 7 200Demand130 170 100 150Formulate this problem as a linear programming model, and solve it by using the computer

Answer 1

Transportation model
This is a type of linear programming model which is used to find the least cost in the shipment or transportation of products from one location to other.
A company grows oranges and stores in warehouses located at L, M, and F. The company supplies oranges from the warehouses to 4 markets N, P, C, and B. Consider the following information about the supply, demand and the cost of shipment per truck load:
  
Formulate the linear programming model and consider the following decision variables:
Decision variable:
Amount of oranges supplies from location i to location j;
Objective function is to minimize the total cost associated with shipment:
  
Supply constraints are subjected to:
  
Note: xMC is not included in the second supply constraint equation because of the agreement between the distributors.
Demand constraints are subjected to:

  
Non-negativity constraints are:
  
Formulate an Excel spreadsheet for warehouses and markets and calculate the total cost of shipment, as shown below:
  
  

  
Select “Solver” from the “Data” menu bar, as shown below:
  
A pop-up window would appear after clicking on “Solver”. Fill in the objective function and constraints as shown below:
  
Click on “Solve” option. Then the following pop-up would appear:

The following results are obtained: