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 ?
$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.