A truck manufacturer has three manufacturing plants and four retail outlets. The details of the demand at outlets, supply at plants, and the cost to transport between plants and outlets in lakhs (a lakh is a unit in the Indian numbering system equal to one hundred thousand) are provided in the table below.

Since the demand exceeds supply, the company plans to construct one more plant (A or B) to fulfil the balance demand. The cost of production at the proposed Plants A and B are given in the table. 

In addition to the above costs, the fixed cost of constructing Plant A is 500 lakhs and Plant B is 600 lakhs. The company wants to minimize its cost, which includes production, transportation, and construction.
a. Formulate an integer programming model for this problem.
b. Solve this model by using the computer.

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Plant 1 Plant 2 Plant 3 Plant A Plant B Demand (trucks) Outlet 1 0.10 0.15 0.22 0.18 0.19 350 Outlet 2 0.12 0.14 0.23 0.22 0.17 400 Outlet 3 0.15 0.18 0.24 0.16 0.13 250 Outlet 4 0.18 0.23 0.18 0.23 0.17 300 Supply (trucks) 300 250 350 Production cost (in lakhs) 15 17 16 18 19