Consider the Primal linear program,

$$

\min _{x_1, x_2 \geq 0} 3 x_1+4 x_2

$$

subject to the constraints,

$$

\begin{aligned}

& x_1+3 x_2 \geq 9 \\

& 2 x_1+x_2 \geq 8 \\

& x_1-2 x_2 \geq 4

\end{aligned}

$$

a) Solve the linear program algebraically or graphically.

b) Verify

c) Write the dual linear program.

d) Solve using Excel

e) Write the complementary slackness conditions for the primal and dual variables.