Question $1$:

Consider the following problem.

max$3x_1+2x_2$

$s.t.3x_1+x_{2}12$

$x_1+x_{2}6$

$5x_1+3x_{2}27$

$x_1,x_{2}0.$

Solve the problem using the simplex method. How many iterations do you need to reach the optimal solution?

What is the optimal solution $($value of $x1,x2$ and $z)?$

Comment on the constraints and resources associated with each constraint. What are the binding and non$-$binding constraints? which resources are scares and which are abundant?