Consider the following linear problem
$$\max tx_1+x_2\\ s.t. 4x_1+3x_2\le12 \\ 3x_1+4x_2\le12\\ x_1,x_2\ge0$$
where the parameter $t$ grows exponentially $t\in[1,\infty).$
Find the sequence of basic optimal solutions.
First we should convert to standar form
$$\max tx_1+x_2\\ s.t.\ 4x_1+3x_2+x_3=12 \\ 3x_1+4x_2+x_4=12\\ x_1,x_2\ge0$$
Then, I am not sure how should I proceed.
I've solved exercise where you have say $3$ instead of $t$ and then you change $3$ by $4$ and then analyze how the final simplex tableau changes, as it is a coefficient of a basic variable the optimality and factibility might both be affected.
But this could be fixed by using again simplex method or dual-simplex in the final tableau.
My question is how should I proceed in this case where there is a $t$ instead of a number?
Could someone help me please?
I would really appreciate any help you're willing to provide. Thank you.