# Convert this problem into linear programming format

This problem is from the book Luenberger "Linear and Non Linear Optimization". I am facing difficulty with this problem. I am trying to follow this logic -

Let $t = \max (c_1^Tx+d_1,....,c_p^Tx+d_p)$. Then as $t$ is the maximum value could I re-write the constraints as this ?

$\min t$

subject to

$c_1^Tx+d_1 \geq t, ....., c_p^Tx+d_p \geq t, Ax = b , x \geq 0$

Is this correct. or else please tell me where I am going wrong.

It should have been than $$c_i^Tx+d_i \leq t$$
as we want $t$ to be an upper bound of $c_i^Tx+d_i$ and the maximal value will be attained as we minimize $t$.