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\begin{document}
\noindent
{\bf Math 323 Operations Research} {\hfill Homework 1 Additional 
problem}


Consider the system of equation:
$$~ x_1 + 2x_2 + 2x_3 + ~x_4 \qquad = 8$$
$$3x_1+4x_2+ ~x_3  \ \quad\quad + x_5 = 7.$$

(a) Find all the 10 solutions such that at least three
 of the variables equal zero.

(b) Determine the solution found in (a) that are nonnegative and
yield

$$\max Z = 5x_1+2x_2+3x_3-x_4 + x_5.$$ 

\end{document} 

