Product of binary and integer constraint - Linear Programming - optimization

Question

I am trying to formulate a linear program that will assign different number of employees to start in different days. Each group of employees starting on a day will get two days off during the week. However, the schedule is unknown. For example, employees starting Monday can be off any two days in the week. Since the number that will start on day (i) is unknown and whether they will have a day off or not is unknown, I will have the product of two decision variables - one is an integer xi (employees starting on day i) and a binary variable yij (whether the employees starting on day i have a day off on day j).
I am done with formulation and here it is:
Decision variables 1: xi (employees starting on day i)
Decision variables 2: yij (1 if employees starting on day i are working on day j, or 0 if employees starting on day i are off on day j)
Objective function:
Minimize total employees-- sum (i in 1..7) xi
Subject to:
xi*yij >= Requiredj (the number of available workers on day j have to satisfy the demand on day j)
I am trying to code this on CPLEX but i dont know how to make xi*yij linear and write the code....can anyone please help me?
Thank you.

Answer 1

In How to with OPL How to multiply a decision variable by a boolean decision variable in CPLEX ?
// suppose we want b * x <= 7
dvar int x in 2..10;
dvar boolean b;
dvar int bx;
maximize x;
subject to
{
// Linearization
bx<=7;
2*b<=bx;
bx<=10*b;
bx<=x-2*(1-b);
bx>=x-10*(1-b);
// if we use CP we could write directly
// b*x<=7
// or rely on logical constraints within CPLEX
// (b==1) => (bx==x);
// (b==0) => (bx==0);
}