Alliance Flour produces commercial all-purpose flour from four plants in the U.S. and ships them to the two biggest bread producers in the country. However, Alliance Flour doesn’t know how to most effectively ship its flour to satisfy their contracted demand for the next month. Alliance Flour’s four manufacturing sites are Los Angeles, Seattle, Chicago, and Boston with a monthly production supply of 8,000, 9,000, 1,000, and 7,000 respectively. The two bread producers are located in Dallas and Orlando with an upcoming monthly demand of 20,000 and 5,000 respectively which Alliance Flour must satisfy. In addition, Alliance Flour does not directly transport its flour as it contracts a shipping company that requires all of Alliance Flour’s production to be sent a distribution center before it is sent to the bread producers. The shipping company has two distribution centers located in Nashville and Denver and they have told Alliance Flour that they can handle at most 24,000 and 11,000 pounds of flour that month respectively.
By using the shipping company, Alliance Flour has contracted the following $/lb to ship its products between all possible destinations:
|Distribution Center (DC)|
|Manufacture site||LosAngeles||$ 4.07||$ 4.21|
|Seattle||$ 3.64||$ 4.70|
|Chicago||$ 3.30||$ 2.53|
|Boston||$ 3.18||$ 2.79|
|DC||Nashville||$ 1.40||$ 2.04|
|Denver||$ 1.66||$ 2.44|
Using this information, complete the following tasks/questions:
Mathematically formulate (i.e. type out or write down) a linear optimization model to minimize Alliance Flour’s transportation costs for the month including all decision variables, the objective function, and all constraints.