Maximizing the Net Present Value (NPV):

According to the given information, a company contains 9 projects under consideration. Each project the NPV is added and the capital required by every project during the next two years.

Now consider “x_i” be the fraction of investment that is undertaken as i = 1, 2, K, 9

The objective function is to maximize the NPV of the investment.

Maximize z=14x1+17x2+17x3+15x4+12x6+14x7+10x8+12x9

Constraint 1:

At 1^st year, $50 million is available for investment.

The expression is:

={(expenditure required during year 1 for project 1)+(expenditure required during year 1 for project 2)+K(expenditure required during year 1 for project 9)}=12x1+54x2+6x3+6x4+30x5+6x6+48x7+36x8+18x9≤50

Constraint 2:

At 2^nd year, $20 million is available for investment.

The expression is:

={(expenditure required during year 1 for project 1)+(expenditure required during year 1 for project 2)+K(expenditure required during year 1 for project 9)}=3x1+7x

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