📘 linear programming

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

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: