Solve the following linear program using the simplex algorithm. You should give the

initial tableau and each further tableau produced during the execution of the algorithm.

If the program has an optimal solution, give this solution and state its objective value. If

it does not have an optimal solution, say why.

You should indicate the highlighted row and columns in each pivot step as well as the

row operations you carry out. This is in order to gain credit even if the final answer is

incorrect.

$mamize,2x_1+3x_2+5x_3+x_4$

subject $to{x}_1+x_2+2x_3+x_{4}2,$

$3x_2+3x_3+3x_{4}6,$

$3x_1+2x_2+2x_3+x_{4}7,$

$x_1,x_2,x_3,x_{4}0$

Suppose that we are carrying out the simplex algorithm on a linear program in

standard inequality form $($with $3$ variables and $4$ constraints$)$ and suppose that we

have reached a point where we have obtained the following tableau. Apply one more

pivot operation, indicating the highlighted row and column and the row operations

you carry out. What can you conclude from your updated tableau?