capacity planning problem

A retail chain is considering whether to expand a distribution center or not.

If so$,$ the level of the expansion should be at least $3000$ units but not more

than $8000$ units. The expansion incurs a high initial cost and the cost of

expansion follows a nonlinear cost function. Disregarding all other information, formulate the expansion decision constraints only.

Decision variables:

X the amount of expansion to be made

y $1$ if the decision for expansion is yes

$0$ if the decision for expansion is no

We will ignore the objective function for the time being and will discuss

it later.

Constraints:

If the decision for the expansion is yes, then it should be at least $3000$ units

but not more than $8000,$ that is

X $>=3000$

X $<=8000$

To incorporate the yes$=$no decision with the above constraints, we rewrite

them as follows:

X $>=3000$y

X $<=8000$y