Question: Question 3: A manufacturer is considering alternatives for building new plants to be closer to its major customer locations. The net cost of manufacturing and transporting each unit of the product to its customers will vary depending on where the plant is built. These data is given below (in $):

The annual demand for the customers X, Y, and Z are expected to be 40.000, 25.000. and 35, 000 units, respectively. The annual production capacity and the construction cost at each location are:

The company wants to determine which plants to open in order to satisfy customer demands at minimum total cost.

a) Formulate the problem as a mixed integer program.

b) How -would you revise the formulation, if you could build a plant as large you want at any location?