if else statement linear programming I am trying to work out an if else statement for the following problem, which should be mathematically linear programmed:
when both item 1 and item 2 are picked, both their costs are reduced with 20%. I have more items than only item 1 and 2, and there costs never change. if only one of item 1 or 2 are picked, there regular costs will be implemented.
I thought of the following, however I don't know how to rewrite it in a way it is mathematical and thus not contains any ifs and whens:
$C_i$: reduced cost of item $i$ for $i \in \{1,2\}$
$K_i$: regular cost of item $i$ for $i \in \{1,2,3,4\}$
$X_i$: whether or not item $i$ is picked for $i \in \{1,2,3,4\}$
the sum of $X_i  C_i$ should be smaller than or equal to $1300$
$C_1 = 0.8K_1$ if $X_1+X_2=2$
$C_2= 0.8K_2$ if $X_1+X_2=2$
$C_i=K_i$ for $i\in \{3,4\}$
Is there anyone who can help me with this?

Normally in these cases we use an auxiliar variable that takes values $\{0,1\}$.
Thus we add the variable $\delta \in \{0,1\}$ that is $1$ if both items are bought and $0$ otherwise. Add the corresponding price to the objective function times $\delta$ and you should be done.
