Allied Manufacturing Has Three Factories Located in Dallas,Houston,and New Orleans

question 82

Essay

Allied Manufacturing has three factories located in Dallas,Houston,and New Orleans.They each produce the same 281 products and ship to three regional warehouses - #1,#2,and #3.The cost of shipping one unit of each product to each of the three destinations is given in the table below: There is no way to meet the demand for each warehouse.Therefore,the company has decided to set the following equally weighted goals: (1)each source should ship as much of its capacity as possible, (2)the number shipped to each destination should be as close to the demand as possible, (3)the capacity of New Orleans should be divided as evenly as possible between warehouses #1 and #2,and (4)the total cost should be less than $1,400.Formulate this as a goal program,which includes a strict requirement that capacities cannot be violated.

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Definitions:

Optimum

The most advantageous condition or degree of something, where the best possible outcome is achieved.

Feasible Region

In optimization problems, it is the set of all possible points that satisfy the problem's constraints, representing all possible solutions.

Corner-point Solution

A method in optimization problems, especially linear programming, where the optimal solution is found at the vertex or corner of the feasible region.

Feasible Region

The set of all possible points that satisfy a problem’s constraints, used in optimization to find the best solution.