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

Assignment 1

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

Minimize $-x_{1}+2x_{2}-x_{3}\,\!$

Subject to

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

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

• Maximize $2x+5y~$

Subject to

${\begin{alignedat}{1}-3x+2y\leq 6\\6x+2y\geq 2\\x,y\geq 0\\\end{alignedat}}~$

• Maximize ...