Question

A new business is hiring managers and employees. The company needs at least 20 managers and no more than 500 employees. It must hire a total of at least 400 people. Write a system of linear inequalities to represent the constraints of this situation. Let x represent the number of managers, and let y represent the number of employees.

Answer 1

We can represent the constraints of this situation with the following system of linear inequalities:

x ≥ 20 (the company needs at least 20 managers)

y ≤ 500 (the company needs no more than 500 employees)

x + y ≥ 400 (the company must hire a total of at least 400 people)

So the system of linear inequalities is:

x ≥ 20

y ≤ 500

x + y ≥ 400