Convert the following model into an LP model. Note that you're not being asked to convert this to standard form.
$$\min z = \max (x_1, x_2, x_3, 2000)$$
s.t. $$-2x_1 + x_2 + x_3 \geq -4$$
$$3x_1 - 4x_2 + x_3 \leq 12$$
$x_i \geq 0$ for all $i$
I am having difficulty thinking through how to set up an objective function that isn't a formula, but selects the maximum of multiple variables. I've tried setting up the $\max(x_1, x_2, x_3, 2000)$ as a matrix and as another variable x4, but it doesn't make sense to me on paper. When I write the problem in Excel, I use
=MAX(x1, x2, x3, 2000) as the objective function but I don't understand the algorithm I would use to solve this problem. I've researched several textbooks and am stuck on setting up an objective function that selects a single maximum value of several variables.