In this model, to solve the problem of the least number of salespeople, the first thing to understand is the distribution mode of salespeople and the number of salespeople needed every day, and the second thing to pay attention to is the arrangement of salespeople taking two consecutive days off.

As can be seen from the problem, the time arrangement of sales staff should be five days' work and two days' rest, followed by five days' work and two days' rest. In order to minimize the staffing, it is necessary to make the work and rest time between salespeople well connected.

Because each salesman works for five days and takes two days off, as long as the number of salesmen who take two days off in a row is calculated, the total number of salesmen is calculated. Divide the salespeople who have rested for two days in a row into seven categories according to the time when they began to rest, and then write down the constraints according to the number of salespeople needed every day, so that we can establish a model and find the best scheme.