📘 linear programming

1. **State the problem:** The farm owner has 140 acres of land to plant corn and soybeans. Each acre of corn yields a profit of 370 and requires 2 hours of labor. Each acre of soyb

1. **State the problem:** Jacob needs to buy meat and cheese to meet minimum weekly requirements of 12 units of carbohydrates and 8 units of protein.

1. **State the problem:** Jacob needs to buy meat and cheese to meet minimum weekly requirements of 12 units of carbohydrates and 8 units of protein. Meat contains 2 units carbs an

1. **State the problem:** We want to find the minimum and maximum values of the objective function $$z = 5x + 4y$$ subject to the constraints: $$2x + y \leq 20$$

1. **State the problem:** Maximize the objective function $$z = 3x + 7y$$ subject to the constraints: $$4x + 6y \leq 24$$

1. **Problem Statement:** We have a linear programming problem (P) with objective function $$w = 5x_1 + \alpha x_2 - x_3$$ and constraints:

1. **State the problem:** Minimize the objective function $$R(x,y) = x + 2y$$ subject to the constraints: $$x + y \geq 2$$

1. **Problem Statement:** We have a primal linear program (P): $$\max w = 5x_1 + 8x_2$$

1. **Stating the problem:** We are given a primal linear programming (LP) problem (P):

1. **State the problem:** We want to derive the dual problem of the given primal linear program:

1. **Problem Statement:** We want to maximize the objective function $$w = 3x_1 + x_2$$ subject to constraints:

1. **Problem Statement:** We have the system of inequalities:

1. **State the problem:** We have the linear programming (LP) problem:

1. **State the problem:** We want to maximize the profit from producing tables (x) and chairs (y) given constraints on available hours in two departments.

1. **State the problem:** We want to determine how many units of products A and B should be produced and sold to maximize total profit, given constraints on raw materials and labor

1. **Problem Statement:** KIA Motors Limited (KML) wants to maximize total sales by sending promotions to two customer groups: current customers and new customers.

1. **State the problem:** We want to maximize the weekly profit from producing two toy guns, Acer ($8 profit per dozen) and Bulls-I ($5 profit per dozen), subject to resource and m

1. The problem is to determine whether to plot the constraint $$y - x \leq 350$$ given that all other constraints intersect in the upper right quadrant except this one. 2. The cons

1. **State the problem:** We want to maximize the weekly profit from producing two toy guns: Acer and Bulls-I.

1. **Stating the problem:** We want to maximize the objective function $$Z = -3x_1 - 2x_2$$

1. Задача: Минимизировать функцию цели $$Z(X) = -2x_1 + x_2 + 3x_3 - 2x_4$$ при условиях: $$\begin{cases} 3x_1 - x_2 - 4x_3 + x_4 = 2, \\ 5x_1 - x_2 - 7x_3 + 2x_4 = 6, \\ x_j \geq