📘 linear programming

1. **Stating the problem:** We are given a system of inequalities:

1. The problem is to minimize the objective function $$z = 40x + 50y$$ subject to the constraints: $$2x + y \geq 24$$

1. The simplex method is used to solve linear programming problems of the form: maximize or minimize a linear objective function subject to linear equality and inequality constrain

1. **State the problem:** We want to maximize the profit function $$\text{Profit} = 5000x + 7000y$$ subject to constraints: