Sitka Manufacturing is planning to build at least one new plant, and three cities are being considered:

Baytown, Texas; Lake Charles, Louisiana; and Mobile, Alabama. Once the plant or plants have been constructed, the company wishes to have sufficient capacity to produce at least 38,000 units each year.

The costs associated with the possible locations are given in the following table.

APPROACH c In modeling this as an integer program, the objective function is to minimize the total of the fixed costs and the variable costs. The constraints are: (1) total production capacity is at least 38,000; (2) the number of units produced at the Baytown plant is 0 if the plant is not built, and it is no more than 21,000 if the plant is built; (3) the number of units produced at the Lake Charles plant is 0 if the plant is not built, and it is no more than 20,000 if the plant is built; and (4) the number of units produced at the Mobile plant is 0 if the plant is not built, and it is no more than 19,000 if the plant is built.
Then, we define the decision variables as

X1 5 number of units produced at the Baytown plant X2 5 number of units produced at the Lake Charles plant X3 5 number of units produced at the Mobile plant

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SITE ANNUAL FIXED COST VARIABLE COST PER UNIT ANNUAL CAPACITY Baytown, TX $340,000 Lake Charles, LA $270,000 Mobile, AL $290,000 $32 $33 $30 21,000 20,000 19,000