📘 linear programming

1. The problem involves deciding how many 100-ounce lots of plastic Parket Sisters should buy at $6.00 per ounce (usual cost $5.00 plus $1.00) and determining the optimal product m

1. **State the problem:** We are given a linear programming (LP) problem (P):

1. **Stating the problem:** We want to maximize the objective function

1. Let's first define the concepts in Linear Programming (LP). 2. Alternative optimal solutions occur when multiple optimal points (solutions) yield the same optimal objective valu

1. **State the problem:** We have two refineries with different costs and production capacities.

1. **Problem Statement:** We need to maximize the objective function $$Z = 2X_1 - X_2 + 2X_3$$ subject to the constraints:

1. **State the problem:** We want to minimize the operating cost of two refineries meeting specific oil production demands.

1. **Problem a:** Minimize $w = x_1 + 2x_2$ given constraints: - $x_1 + x_2 \leq -1$

1. **State the problem:** Maximize \( w = -2x_1 + 5x_2 \) subject to: \( x_1 + x_2 \leq 6 \)

1. **State the problem:** Maximize $$w = -2x_1 + 5x_2$$ subject to constraints: $$

1. **Problem Statement:** We have the linear programming problem with objective function $w = \alpha x_1 + x_2$ and constraints:

1. **Problem statement:** We want to maximize $4x_1 + x_2$ subject to the constraints:

1. **State the problem:** We want to minimize the objective function $$Z = 2x_1 + 4x_2$$ subject to the constraints: - $$5x_1 - 3x_2 \geq 15$$

1. **State the problem:** Minimize $Z = 2x_1 + 4x_2$ subject to

1. Diketahui dua campuran logam dengan komposisi per ton (1000 kg): - Campuran I: 50 kg logam utama, 80 kg logam P, 40 kg logam Q

1. **Stating the problem:** We are given a system of inequalities:

1. The problem is to minimize the objective function $$z = 40x + 50y$$ subject to the constraints: $$2x + y \geq 24$$

1. The simplex method is used to solve linear programming problems of the form: maximize or minimize a linear objective function subject to linear equality and inequality constrain

1. **State the problem:** We want to maximize the profit function $$\text{Profit} = 5000x + 7000y$$ subject to constraints: