📘 linear programming

1. **State the problem:** We want to maximize

1. **State the problem:** We want to maximize the objective function $$Z = -4x_1 + 6x_2 - 18x_3$$

1. **Problem statement:** We have the feasible region $$S = \{(x_1,x_2) \in \mathbb{R}^2 : -x_1 - x_2 \leq 1, -x_1 + 2x_2 \geq 2, x_1 - x_2 \leq -1, x_1 \leq 0, x_2 \geq 0\}$$

1. **Problem statement:** We have the feasible region $S = \{(x_1,x_2) \in \mathbb{R}^2 : -x_1 - x_2 \leq 1, -x_1 + 2x_2 \geq 2, x_1 - x_2 \leq -1, x_1 \leq 0, x_2 \geq 0\}$ and wa

1. The problem is to understand what "basic feasible" means in the context of linear programming. 2. In linear programming, a "feasible solution" is any solution that satisfies all

1. **Problem Statement:** We have two optimization problems: (a) a maximization problem and (b) a minimization problem, each with objective functions and constraints.

1. **Problem Statement:** We want to determine how many REGULAR and SUPER tents to manufacture weekly to maximize profit, given labor hour constraints and demand limits.

1. **Problem Statement:** We want to determine how many REGULAR tents ($x$) and SUPER tents ($y$) to manufacture weekly to maximize profit, given labor hour constraints and demand

1. **Problem Statement:** A farmer wants to minimize the daily cost of chicken feed using two types of feed, A and B.

1. **State the problem:** Minimize $$z = 2x_1 + 3x_2$$

1. **State the problem:** We want to minimize $$z = 2x_1 + 3x_2$$ subject to constraints:

1. **State the problem:** We want to maximize the objective function $$Z = 2x_1 + 10x_2$$

1. **Problem Statement:** A firm manufactures two products with profits of 3 and 5 per unit respectively. Each product requires processing time in two departments D1 and D2. Produc

1. **Problem Statement:** Minimize $$z = 4x_1 + 4x_2 + x_3$$ subject to: $$2x_1 + x_2 + 3x_3 \leq 2$$

1. **State the problem:** We need to minimize the cost function $$\text{Cost} = 1.80S + 2.20T$$ subject to the constraints: $$5S + 8T \geq 200$$

1. **State the problem:** We want to minimize the cost function $$P = 1.80S + 2.20T$$ subject to the constraints: $$5S + 8T \geq 200$$

1. **Stating the problem:** We want to maximize the power output function $$Z = 400X + 300Y$$ where $$X$$ and $$Y$$ represent the number of Monocrystalline and Polycrystalline sola

1. **Problem Statement:** We are given a linear programming problem to minimize the cost function $$\text{Cost} = 1.80S + 2.20T$$ subject to the constraints: $$5S + 8T \geq 200$$

1. **Problem Statement:** We have three loan products: Personal (P), Business (B), and Housing (H). Each requires certain resources (Officers, Compliance hours, Risk assessments) a

1. **Problem Statement:** Find the new optimal solution for the linear program when the objective function changes to:

1. **Problem Statement:** We want to maximize the profit from producing Alloy Gamma (x tons) and Alloy Delta (y tons) given constraints on raw materials Copper, Zinc, and Nickel.