Chapter 3.6, Problem 4P

Explanation of Solution

 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 $z=14x_1+17x_2+17x_3+15x_4+12x_6+14x_7+10x_8+12x_9$

 Constraint 1:

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

 The expression is:

 $\begin{array}{l}=\left\{\begin{array}{l}\left(\text{expenditure required during year 1 for project 1}\right)+\\ \left(\text{expenditure required during year 1 for project 2}\right)+\\ K\left(\text{expenditure required during year 1 for project 9}\right)\end{array}\right\}\\ =12x_1+54x_2+6x_3+6x_4+30x_5+6x_6+48x_7+36x_8+18x_9\le 50\end{array}$

 Constraint 2:

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

 The expression is:

 $\begin{array}{l}=\left\{\begin{array}{l}\left(\text{expenditure required during year 1 for project 1}\right)+\\ \left(\text{expenditure required during year 1 for project 2}\right)+\\ K\left(\text{expenditure required during year 1 for project 9}\right)\end{array}\right\}\\ =3x_1+7x_{}\end{array}$