A petroleum refinery in Dubai wants to expand its refinery and stock-yard for the expected surge in the oil prices in the coming years. The company has four distinct activities in its strategic plan—plant expansion, stockyard improvement, adopting modern technology and research and development. Each of the different activities has a cost and an expected NPV. The following table lists the costs, available capital, and NPV of each activity required to execute each of the options in millions of dirhams.

The company wants to maximize it’s net present value considering its budgetary constraints.
a. Formulate an integer programming model for this problem.
b. Solve this model by using the computer.

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Year 1 Year 2 Year 3 Year 4 NPV (million AED) Plant expansion (million AED) 22 18 20 20 80 Stockyard improvement 20 19 20 17 Adopting modern (million AED) AED) 15 25 26 50 technology Research and (million development (million AED) 20 20 30 36 40 30 Available capital (million AED) 60 62 67 40