📘 linear programming

1. Задача: Максимизировать функцию цели $$Z(X) = 3x_1 - x_2$$ при ограничениях: $$-3x_1 + 2x_2 \leq 6,$$

1. **State the problem:** Minimize the objective function $$Z = 4x + 3y$$ subject to the constraints: $$2x + y \geq 10$$

1. **Problem Statement:** Angela and Zooey want to decide how many fish dinners ($x$) and beef dinners ($y$) to prepare each night to maximize profit, given constraints on total me

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

1. **State the problem:** Reduce the given linear programming problem to its standard form.

1. **State the problem:** We want to maximize the profit from products A and B given constraints on sales, availability, and raw material usage.

1. **Problem Statement:** An investor wants to invest in two companies: Company 1 (extractive) and Company 2 (tech). Prices per share are $40$ for Company 1 and $25$ for Company 2.

1. **Stating the problem:** Maximize $$Z = 4x_1 + 3x_2 + 2x_3$$

1. **Stating the problem:** We want to solve the linear programming problem:

1. **State the problem:** We want to maximize an objective function subject to constraints with $x_1 > 0$ and $x_2 > 0$. However, the objective function and constraints are not ful

1. **Problem Statement:** Formulate and solve the linear programming (LP) model to maximize profit from chairs and tables made with limited resources.

1. **Problem statement:** Rehema has 900 tonnes of bricks at Mtakuja and 600 tonnes at Tupendane. She wants to transport bricks to sites A, B, and C requiring 500, 600, and 400 ton

1. **State the problem:** Find the maximum value of $Z = 4x + 3y$ subject to the constraints:

1. **State the problem:** We need to maximize the objective function $$Z = 6x + 5y$$ subject to the constraints: $$x \geq 0,$$

1. **State the problem:** We want to maximize the objective function $$Z = 6x + 5y$$ subject to the constraints:

1. The problem is to maximize the objective function $Z = 3x + 5y$ given the corner points of the feasible region: $(0,0)$, $(0,6)$, $(4,4)$, and $(6,0)$. 2. We will evaluate $Z$ a

1. Problem Statement: Formulate a linear programming model to maximize the total return from investing in two companies, given investment constraints.

1. The problem is to understand and describe the feasible region for a given system of inequalities or constraints in an optimization or linear programming problem. 2. The feasible

1. **Problem Statement:** We want to determine the number of shares of Company 1 and Company 2 an investor should buy to maximize returns while satisfying investment constraints. 2

1. Misalkan kita pilih soal (a): Maksimumkan fungsi tujuan

1. **State the problem:** We want to maximize the profit from producing two products A and B.