📘 linear programming

1. **State the problem:** Maximize $30x + 50y$ subject to constraints:

1. **Problem Statement:** Maximize the objective function $$30x + 50y$$ subject to the constraints: $$3x + 4y \geq 12$$

1. **Problem Statement:** We have two crops, Maize and Soybean, with constraints on land, labor, and nitrogen resources. We want to maximize returns.

1. **State the problem:** We want to determine how many wrenches ($x$) and pliers ($y$) to produce to maximize profit given constraints on steel, machine hours, and demand.

1. **State the problem:** We want to minimize the objective function $$Z = 3x_1 + 4x_2$$ subject to the constraints:

1. **State the problem:** We want to maximize the objective function $$Z = x_1 + 9x_2 + x_3$$

1. **Problem Statement:** We want to determine the number of units of products A ($X_1$) and B ($X_2$) to produce weekly to maximize profit.

1. **Problem Statement:** MetroLink Seating is designing a seating layout for a passenger car with Premium and Standard sections. Each Premium section yields a profit of 600 and re

1. **State the problem:** We want to minimize the objective function $$Z = 5x_1 + 3x_2$$ subject to the constraints:

1. **State the problem:** We want to minimize the objective function $$Z = 5x_1 + 3x_2$$ subject to the constraints:

1. **State the problem:** We want to maximize the objective function $$Z = 2x_1 + 3x_2$$ subject to the constraints:

1. The problem states that the feasible region of a linear programming problem is bounded and the objective function attains its minimum value at more than one point. 2. One of the

1. **Problem Statement:** Maximise the objective function $$Z = 3x + 2y + 1$$ subject to the constraints $$x \geq 0$$, $$y \geq 0$$, and $$3x + 4y \leq 12$$. We need to identify th

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