📘 linear programming

1. **Problem Statement:** Solve the Linear Programming Problem (L.P.P.) by the Simplex method:

1. **Problem Statement:** Mary wants to maximize her profit by baking two types of cakes: Special and Standard. She makes 70 profit per Special cake and 50 profit per Standard cake

1. **State the problem:** We want to maximize the profit from manufacturing chairs, tables, and bookcases given constraints on cutting, assembly, and finishing hours.

1. **Problem Statement:** A jewelry store has 18 ounces of gold and 20 ounces of platinum. Each necklace requires 3 ounces of gold and 2 ounces of platinum. Each bracelet requires

1. **State the problem:** We want to determine how many necklaces and bracelets to make to maximize profit, given constraints on gold, platinum, and demand.

1. **State the problem:** We want to maximize $x_2$ subject to the constraints:

1. Problem 1: Maximize profit for gadgets A and B with labor constraints. 2. Define variables: Let $x$ = number of Gadget A produced, $y$ = number of Gadget B produced.

1. The problem is to find the coefficients of each variable $x_1, x_2, x_3, x_4, x_5$ in the objective function and constraints of the given linear optimization problem. 2. The obj

1. **State the problem:** We are given a primal linear programming problem:

1. **State the problem:** We want to determine how many posters ($x$) and flyers ($y$) the printing shop can produce given time constraints for designing and printing, and also cal

1. **Problem Statement:** We analyze regions defined by inequalities and maximize given linear objectives over these regions.

1. **Problem Statement:** A firm operates two plants, A and B, producing cakes, pellets, and meal. We want to find how long each plant should run to meet orders of 2000 tonnes of c

1. **Problem Statement:** We need to solve the linear programming problem:

1. **Problem Statement:** We need to maximize the objective function $$Z = 4x + 3y$$ subject to the constraints:

1. **State the problem:** We want to maximize the objective function $$Z = 4x + 3y$$ subject to the constraints:

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

1. **Stating the problem:** We are given the objective function $$z = 5x + 3y$$ and the constraints:

1. **State the problem:** A farmer wants to buy bags of two types of animal feed, Type A and Type B, to meet minimum nutritional requirements and minimize cost. 2. **Define variabl

1. **State the problem:** We want to find the maximum value of the function $$z = 4x + 3y$$ subject to the constraints: $$x \geq 4$$

1. **State the problem:** We need to solve the Linear Programming Problem (LPP) using the Big-M penalty method.

1. **State the problem:** We want to maximize the objective function $$Z = 3x_1 - x_2$$ subject to the constraints: