Assignment 1
1. Write the following linear programming problem in standard form.
Minimize
Subject to
![{\displaystyle {\begin{alignedat}{1}3x_{1}+x_{2}+4x_{3}\geq 12\\2x_{1}+4x_{2}=6\\x_{1},x_{2}\geq 0\\x_{3}\leq 8\\\end{alignedat}}~}](https://wiki.ubc.ca/api/rest_v1/media/math/render/svg/8233a7ab317badbdcea16a4bdc1c2be2cd0d642e)
2. For the two linear programming problems below, decide which is infeasible and which isunbounded. In each case justify your answer.
- Maximize
![{\displaystyle 2x+5y~}](https://wiki.ubc.ca/api/rest_v1/media/math/render/svg/654b9bd86beef5585053a36670053ab6544d7c80)
- Subject to
![{\displaystyle {\begin{alignedat}{1}-3x+2y\leq 6\\6x+2y\geq 2\\x,y\geq 0\\\end{alignedat}}~}](https://wiki.ubc.ca/api/rest_v1/media/math/render/svg/3a497a7d073aaa05c05c6da45fc131852c8064b0)