问题94: 单纯形法Minimize 4x1−3x2+2x3−x4 Subject to x1+2x2+3x3+4x4≤10, −x1+x2−x3+x4≤10x1,x2,x3,x4≥0

Minimize $4 x_1-3 x_2+2 x_3-x_4$
Subject to

$$ \begin{aligned} & x_1+2 x_2+3 x_3+4 x_4 \leq 10 \\ & -x_1+x_2-x_3+x_4 \leq 10 \\ & x_1, x_2, x_3, x_4 \geq 0 \end{aligned} $$

(a) Solve the problem by the simplex method.
(b) Find the dual linear program.
(c) Using the complementary slackness condition, find an optimal solution of the dual problem.