Quantitative Analysis for Management, 13/e

Solved Problems

1. Solved Problem 10-1 Consider the 0–1 integer programming problem that follows:

   $$\begin{array}{ll}\text{Maximize}\hfill & 50X_1+45X_2+48X_3\hfill \\ \text{subject to}\hfill & 19X_1+27X_2+34X_3\le 80\hfill \\ 22X_1+13X_2+12X_3\le 40\hfill \\ X_1,X_2,X_3\text{must be either 0 or 1}\hfill \end{array}$$

   Now reformulate this problem with additional constraints so that no more than two of the three variables can take on a value equal to 1 in the solution. Further, make sure that if $X_1=1$, then $X_2=1$ also. Then solve the new problem using Excel.

   Solution

   Excel can handle all-integer, mixed-integer, and 0–1 integer problems. Program 10.12 shows two new constraints to handle the reformulated problem. These constraints are

   $$X_1+X_2+X_3\le 2$$

   and

   $$X_1-X_2\le 0$$

   The optimal solution is $X_1=1, X_2=1, X_3=0$, with an objective function value of 95.

   Program 10.12 Excel 2016 Solution ...