📘 linear programming

1. **State the problem:** We want to maximize the objective function $$P = 35x_1 + x_2$$ subject to the constraints:

1. **State the problem:** Graph the system of inequalities:

1. **State the problem:** We want to maximize the objective function $$P = 22x_1 + 11x_2$$

1. **State the problem:** Graph the system of inequalities:

1. **State the problem:** Convert the inequality system to an equation system using slack variables and find all basic solutions, indicating feasibility. 2. **Convert inequality to

1. **State the problem:** Convert the inequality system to an equation system using slack variables and write the associated linear equation. 2. **Given inequality:**

1. **State the problem:** We are given six basic solutions to the system: $$\begin{cases} 2x_1 + 3x_2 + s_1 = 9 \\ 4x_1 + 3x_2 + s_2 = 12 \end{cases}$$

1. **State the problem:** We have the system of equations: $$2x_1 + 3x_2 + s_1 = 162$$

1. **State the problem:** We want to maximize the objective function $$P = 6x_1 + 2x_2$$ subject to the constraint $$7x_1 + 9x_2 \leq 35$$ and non-negativity conditions $$x_1, x_2

1. **State the problem:** We want to convert the inequalities of the linear programming problem into equations by adding slack variables.

1. **State the problem:** We need to write the equation associated with the inequality $$7x_1 + 6x_2 \leq 13$$ by introducing a slack variable $$s_1$$. 2. **Explain slack variables

1. **State the problem:** We want to maximize the objective function $$P = 8x + 8y$$

1. **State the problem:** We want to minimize the cost function $$C = 11x + 8y$$ subject to the constraint $$6x + 7y \geq 84$$ and $$x, y \geq 0$$. 2. **Understand the constraint:*

1. **State the problem:** We want to maximize the objective function $$P = 10x + 70y$$ subject to the constraint $$x + 5y \leq 20$$ and the nonnegativity conditions $$x \geq 0, y \

1. **State the problem:** A farmer has 1000 acres of land to plant wheat and barley. Wheat requires 2 hours of labor per acre, barley requires 1 hour per acre, and the farmer has 1

1. **Stating the problem:** Melanie wants to model constraints for cycling and aerobic stepping using linear programming.

1. **Problem statement:** We want to find the number of turkeys ($x$) and hams ($y$) to distribute such that:

1. **Problem Statement:** A farmer wants to mix two types of food, A and B, to meet minimum daily nutritional requirements at minimum cost.

1. **Problem Statement:** A farmer wants to mix two types of food, A and B, to meet minimum daily nutritional requirements at minimum cost.

1. **Stating the problem:** A company manufactures two products, Product A and Product B. Each unit of Product A requires 3 hours of labour and 4 units of raw material, while each

1. The problem asks to identify the feasible region in a typical Linear Programming Problem (LPP). 2. In LPP, the feasible region is defined as the set of all points that satisfy a