Stoller Manufacturing Company produces fuel injection assembly units for automobile and light truck manufacturers at its facility in Evanston, Arkansas. The company has experienced rapid growth in recent years and is planning to build at least one new plant. Three cities are currently being considered: Baytown, Texas; Lake Charles, Louisiana; and Mobile, Alabama. Once the plant or plants are completed and on line, Stoller Manufacturing wants to have sufficient new capacity to produce at least 38,000 units each year. The Baytown facility would have an annual fixed cost of $340,000 and a production capacity maximum of 21,000 units. The annual fixed cost for the Lake Charles facility would be $270,000 with a maximum production capacity of 20,000 units. The Mobile facility would be able to produce a maximum of 19,000 units and the annual fixed cost would be $290,000. The variable cost per unit at each of the facilities is projected to be $32, $33, and $30 at the Baytown, Lake Charles, and Mobile locations respectively.

a. Formulate an appropriate linear programming model that can be used to determine the optimal number and location of any new facility or facilities to complement the production capacity for Stoller Manufacturing.

Here are my Decision Variables:

Let X1= 1 if a plant is constructed in Baytown, TX facility; 0 if not

X2= 1 if a plant is constructed in Lake Charles, LA facility; 0 if not

X3= 1 if a plant is constructed in Mobile, AL facility; 0 if not

X4= units produced by Baytown, TX facility

X5= units produced by Lake Charles, LA facility

X6= units produced by Mobile, AL facility

Therefore:

Min Z= 340X1+270X2+290X3+32X4+33X5+30X6

s.t.

What would the constraints be? This is a Linear Programming Integer Model.