📘 linear programming

1. **State the problem:** Identify which of the given constraints is NOT a type of constraint in Linear Programming Problems (LPP). 2. **Recall types of constraints in LPP:**

1. **Stating the problem:** Maximize the objective function $$z(x) = 8x_1 + 5x_2$$ subject to the constraints:

1. **State the problem:** We want to minimize the objective function $$f = x_1 + x_2 + 3x_3 + 2x_5$$ subject to the constraints:

1. **State the problem:** We want to minimize the objective function $$f = x_1 + x_2 + 3x_3 + 2x_5$$

1. **State the problem:** We want to maximize the objective function $$f = x_1 + x_2$$ subject to the constraints:

1. **State the problem:** We want to maximize the objective function $$f = x_1 + x_2$$ subject to the constraints:

1. **State the problem:** We want to maximize the objective function $$f = x_1 + x_2$$ subject to the constraints:

1. **State the problem:** We want to maximize the objective function $$f = x_1 + x_2$$ subject to the constraints:

1. **State the problem:** We want to minimize the objective function $$f = x_1 + x_2 + 3x_3 + 2x_5$$ subject to the constraints:

1. **State the problem:** We want to minimize the objective function

1. **State the problem:** We are asked how many lines will be in the graph of the linear program with constraints: $$9P + 5Q \geq 45$$

1. **Énoncé du problème :** Maximiser la fonction objectif $$Z = 390x + 420y + 440z$$

1. **State the problem:** We want to maximize the objective function $$Z = 3X + 5Y$$ subject to the constraints:

1. **State the problem:** We need to transport 1000 men and 84 tonnes of equipment using two types of aircraft: Buffalo and Kestel. 2. **Define variables:** Let $x$ be the number o

1. **State the problem:** We need to transport 1000 men and 84 tonnes of equipment using two types of aircraft: Buffalo and Kestel. 2. **Define variables:** Let $x$ be the number o

1. **State the problem:** We need to solve the first linear programming problem using the graphical method:

1. **Problem Statement:** We want to maximize the total profit from producing cakes and pastries given constraints on baking and decoration hours.

1. **State the problem:** We want to maximize the objective function $$Z = x_1 + 9x_2 + x_3$$ subject to the constraints:

1. **State the problem:** We want to maximize the objective function $$Z = x_1 + 9x_2 + x_3$$

1. **Problem Statement:** A company produces three products X, Y, and Z. Each product requires time on three machines: Turning, Milling, and Grinding. The available machine hours a

1. **State the problem:** Minimize $$z = 2x + 3y$$