📘 linear programming

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 $$z = 2x + 3y$$

1. **Stating the problem:** We have two types of dinghies: Fiberglass and Wooden-hulled.

1. **State the problem:** A boatbuilding firm makes two types of dinghy: fiberglass and wooden-hulled. Fiberglass dinghies sell at a profit of 13 each and require 2 craftsmen and 3

1. **Problem Statement:** A dietician wants to mix two foods to get at least 8 units of vitamin A and 10 units of vitamin C in the mixture. Food I has 2 units/kg vitamin A and 1 un

1. **Problem 1: Determine the feasible solution of the system of linear inequalities:** Given inequalities:

1. **Stating the problem:** We want to maximize the objective function $$z = 3x + 2y$$ subject to the constraints:

1. **Problem Statement:** We want to formulate a linear programming (LP) model for a Baby Food Manufacturing Company that produces two products, x and y, to maximize profit.

1. **Muammo bayoni:** Berilgan chiziqli tenglamalar tizimi va cheklovlar asosida quyidagi chiziqli dasturlash masalasini grafik usulda yechish kerak:

1. **Problem Statement:** We want to maximize the profit from producing tables and chairs given limited hours in carpentry and painting departments.