A manufacturer produces printers at plants in New Orleans, Albuquerque, and Nashville. These are sent to regional distributors in Jacksonville, Boise, and Charlotte. The shipping costs vary, and the company would like to find the least-cost way to meet the demands at each of the distribution centers.
Jacksonville needs to receive 750 printers per month, Boise needs 650, and Charlotte needs 250. New Orleans has 800 printers available each month, Albuquerque has 500, and Nashville has 350.
The shipping cost per unit from New Orleans to Jacksonville is $8, to Boise is $12, and to Charlotte is $7. Due to truck capacity limits, no more than 100 printers can be shipped between New Orleans and Charlotte each month.
The cost per unit from Albuquerque to Jacksonville is $10, and to Charlotte is $9. Printers from Albuquerque are never shipped to Boise. The cost per unit from Nashville to Jacksonville is $11, to Boise is $9, and to Charlotte is $12.
(a) Formulate a linear optimization model to determine how many units should be shipped from each plant to each regional distribution center.
Decision Variables:
Objective Function:
Constraints:
Capacity Constraints:
Demand Constraints:
Non-Negativity Constraints:
(b) Is the capacity of the plants equal to the demand at the distribution centers?
(c) Enter your model in Excel and use Solver to find the optimal distribution plan.
Include your spreadsheet with your homework submission.
(d) What is the optimal distribution plan?
(e) What is the cost of the optimal distribution plan?