Course:MATH340/Archive/2010-2011/921/Assignments

Assignment 1

1. Write the following linear programming problem in standard form.

Minimize $- x_{1} + 2 x_{2} - x_{3}$

Subject to

\begin{aligned} 3 x_{1} + x_{2} + 4 x_{3} \geq 12 \\ 2 x_{1} + 4 x_{2} = 6 \\ x_{1}, x_{2} \geq 0 \\ x_{3} \leq 8 \end{aligned}

2. For the two linear programming problems below, decide which is infeasible and which isunbounded. In each case justify your answer.

Subject to

\begin{aligned} - 3 x + 2 y \leq 6 \\ 6 x + 2 y \geq 2 \\ x, y \geq 0 \end{aligned}