1. [20 points] A mattress manufacturer has three production facilities located in Pittsburg (PA), Houston (TX), and Los Angeles (CA). They supply their products to three distribution centers in Boston (MA), Atlanta (GA), and San Jose (CA). Each distribution center has specific demands to meet. The capacity, demand, and transportation cost per unit between facilities are given in the following map:

For example, the capacity of Los Angeles facility is 1000 units. Demand of San Jose distribution center is 1100 units. Transportation cost per unit from Los Angeles to San Jose is $4.

Develop appropriate linear programming solver, determine how many units should be shipped from each production facility to each distribution center to meet demand while minimizing transportation costs. Calculate the total transportation cost for this distribution plan op a linear programming model defining the decision variables, objective function, and constraints.

Using an appropriate linear programming solver, determine how many units should be shipped from each production facility to each distribution center to meet demand while minimizing transportation costs. Calculate the total transportation cost for this distribution plan.

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