Consider the following problem:

Max$=2^{**}x1+7^{**}x2+4^{**}x3$;

Subject to:

$x1+2^{**}2+310$

$3^{**}1+3^{**}2+2^{**}310$

$x10,x20,x30$

$($i$)$ Develop the dual model and indicate the nature of the dual variables.

$($ii$)$ Solve the dual model graphically and report the optimal solution

$($iii$)$ Use the Complimentary Slackness theorem to find the optimal primal solution. Show

that the optimal objective function values are equal.

$($iv$)$ Identify a feasible solution for the primal as well as for the dual problem and validate

the weak duality theorem.

$($v$)$ Reformulate the dual model with following changes: $($i$)$ The first primal constraint is $>=$

type of inequality, $($ii$)$ the second constraint is an equality and $($iii$)x3$ is an unrestricted

variable. The dual model developed in part $($i$)$ is not in the standard form.

$($vi$)$ Solve the primal and dual problems using the Lingo and report the optimal solutions.